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A TREATISE 



ON 



PEDAGOGICS 



Prfparfd for Students of 

The Inti-rnational Correspondknce Schools 

SCRANTON, PA. 



ARITHMETIC 

GRAMMAR 

GEOGRAPHY 

HISTORY 

ORTHOGRAPHY 

WITH gUHSTIONS ON EACH SUBJECT 



First Edition 



SCRANTON 

THE COLLIERY ENGINEER CO. 
1900 



1. . 

s' ,' 



18514 



Library mT C*ogrre«a 

Two Copies Rechvcd 
JUL 12 1900 

OpycigMMlry 

sEcuNoconr. 






0IU)£I<DI¥6I0N, 

llil 13 I9QQ 



^' 



Copyright, 1900, by THE Coli.ierv Engineer Comr 



Pedagogics o Arithmetic : Copyright, 1897, by THE Coi.lieky Engineer Company 
Pedagogics of Grammar: Copyright, 1898, by The Colliery Engineer Company' 
Pedagogics of Geography: Copyright, 1900. by The Colliery Engineer 

Company. 
Pedagogics of History : Copyright, 1898, by The Colliery Engineer Company 
Pedagogics ot Orthography: Copyright, 1898, by The COLLIERY Engineer 

Company. 



■^lo^e 



Press of Eaton & Mains 
new ^-ork 



— / / 



^3 

PREFACE. 



This Course consists of five distinct Papers, which together 
cover the Pedagogics of theniost important common-school 
branches — Arithmetic, Grammar, Geography, History, and 
Orthography. Every one acquainted with the theory or the 
practice of teaching knows that the subjects mentioned above 
are those in which a young teacher needs help more than in 
any or all others, and that if a teacher can handle these 
branches skilfully, he may be reasonably certain of success 
in teaching any other study with which he is familiar. We 
are told that the most difficult . part of any work is the 
beginning; and since the five branches of this Course lie at 
the very threshold of all common-school work, it has been 
deemed important to make the treatment of each subject as 
thorough, helpful, and practical as possible. 

The student will find that this Course is not a mere com- 
pilation of what other pedagogical writers have said; it con- 
tains, indeed, much about which educators are agreed, but 
besides, there are many matters that are luiique, gleaned 
by the author during inany years' experience as teacher or 
supervisor of teachers. In the narrow compass of a preface 
it would of course be impossible to indicate these distinguish- 
ing features. It must suffice to mention the method of 
mapping complex and compound sentences so as to reveal 
their structure with respect to their component clauses — a 
very valuable and important exercise that, so far as the 
author knows, is entirely new. Another feature is a system 
of minute sentence analysis that has the peculiar merit of 
not dismembering the sentences to which it is applied, thus 
avoiding the criticism by Dr. Bain and many other educators. 
Again, in the treatise on Arithmetic the student will find a 
veiy explicit scheme of elementary fraction work and many 

iii 



iv 1M<1-.FACE. 

practical drill exercises that arc believed to be indispensable 
to thoroughness in fundamentals. The treatment of short 
methods and eavSy labor-saving devices in number work will 
be foimd worth more than the price of the entire Course. 

The index is full and complete, and will be found verv 
iiseful in locating particular portions of the text to which it 
is desired to refer. Each Paper is paged from 1 on, and is 
identified in the index by a number printed at the top of 
each page on the headline, opposite the page number. To 
distinguish this number from the page number, it is pre- 
ceded by the ])rinter's section mark §. Consequently, a refer- 
ence such as i; ;>, page '^0, will be readily found by looking 
through the volume, at the inside edges of the headlines, 
until § 3 is found, and then through § '.] until ixige 20 is found. 

The Question Papers have the same section numbers as 
the Instruction Papers to which they refer, and are grouped 
at the end of the volume. 

Till', In ri'.RN AllONAI, CoKKKSroNDKNCF, vScnooi.S. 



CONTENTS. 



Pkdaoogics of AkrriiMKTic. Section. Page. 

Introducticjn 1 1 

General Remarks . 1 1 

Fundamental Drills 1 28 

Drill Work for Addition 1 28 

Drill Work for vSubtraction 1 28 

Drill Work for Miiltiplieation .... 1 32 

Drill Work for Division 1 ' o'-\ 

Notation and Numeration 1 38 

Arabic Notation 1 38 

Roman Notation 1 4G 

The Teaching of Fractions 1 48 

Matter and Method 1 48 

Primary Work in Detail 1 09 

Preliminary Observations 1 0!) 

Advanced Work 2 1 

Devices and Methods in Advanced Work 2 1 

Addition and Subtraction 2 1 

Short Methods in Multiplication ... 2 G 

Short Methods in Division 2 If) 

Proofs of Fundamental Operations . . 2 2(; 
Signs Used in the Fimdamental Opera- 
tions 2 2!) 

Miscellaneous Operations and vSugges- 

tions 2 30 

Properties of Numbers 2 33 

Factors, Divisors, and Muliiplcs ... 2 38 

Fractions 2 45 

V 



vi CONTENTS. 

Pedagogics of Arithmetic — Continued. Section. Pairc. 

Denominate Nunibers 2 58 

Percentage 2 71 

Interest 2 78 

Interest Laws of Canada t ;i4 

Interest Laws of the United States . . 2 Ito 

Proportion 2 IJO 

Evolution 2 1)8 

Mensuration 2 110 

Miscellaneous 2 113 

Pedagogics of Grammar. 

Introduction 3 1 

General Remarks ■. . 3 1 

Textbooks 3 5 

The Sentence 3 17 

General Considerations ...... 3 17 

Analysis of Sentences 3 27 

Meaning of Terms 3 37 

Ambiguity 3 41 

Synthesis 3 4G 

Summary 3 5(5 

Special Constructions 3 58 

False Syntax 3 60 

Acquiring a Vocabulary 3 G3 

Etymology and Syntax 3 67 

Preliminary Remarks 3 67 

The Noun 3 70 

. The Pronoun 4 4 

The^ Adjective 4 10 

Inflection of Adjectives 4 17 

Anglo-Saxon Prefixes ....'... 4 25 

Latin .Prefixes 4 26 

Greek Prefixes 4 27 

The Verb 4 29 

Classification of Verbs 4 32 

Modes of Verbs 4 43 

The Participles 4 55 



CONTENTS. 



Vll 



Pedagogics of Grammar — Continued. Section. 

The Tenses of Verbs 4 

The Adverb 4 

The Preposition 4 

The Conjunction . 4 

The Interjection 4 



Pedagogics of Geography. 

Educational Values 

Geographical Matter 

Divisions and Definitions .... 
Concepts in Elementary Science 
Sensation and Perception .... 

General Information 

. Collections in Natural Science . . . 
Geography Without a Textbook 
Measures and Their Applications . 
Making and Recording Observations 

Graphic Geography 

Matter and Method in Geography . 

Books of Reference 

Books of Travel and Adventure 
Miscellaneous Books on Travel . 

Pedagogics of History. 

Introduction 

Preparation for Teaching History . 

Methodology 

Description of Methods 

Relation of History to Other vSubjects 
Correlations of History 



Pedagogics of Orthography. 

Introduction 7 

Definitions and Classifications .... 7 

Modification of Words 7 

Compounding of Words ...... 7 

Abbreviations and Contractions ... 7 



Page. 
58 
73 

7!) 
85 
88 



1 

26 

3G 

40 

40 

48 

60 

68 

'68 

81 

95 

108 

132 

133 

134 



1 
14 
26 
26 
61 
64 



1 

1 

20 

20 

31 



viii CONTENTS. 

Pedagogics op' Orthography — Continued. Scctio)i. Page. 

Form and Punctuation of Abbreviations . T 31 

General Considerations on Spelling . . 7 37 

Principles and Materials 7 37 

Methods in Orthography 7 82 

Approved Devices and Word Lists . . 7 82 

Section. 

Questions on Arithmetic 1 and 2 

Questions on Grammar 3 and 4 

Questions on Geography 5 

Questions on History 6 

Questions on Orthography 7 



PEDAGOGICS OF ARITHMETIC 

(PART 1.) 



INTRODUCTION. 



GENERAIi REMARKS. 

1. Tlie Term ••' Peda4>:ogics." — The word pedagogics is 
derived from the Greek TTai.dayoytKf], paidagogikc, which 
means "the art of training or teaching-." The term is com- 
pounded of two simpler words, iraidoq, paidos, "of a boy, " 
and aywyoV, agogos, "a leader." Literally, therefore, a 
pedagogue is a bo/s leader, and pedagogics is the art of 
leading or guiding boys. 

In ancient Greece, boys only were educated, and this 
work was usually entrusted to a slave, who was a constant 
attendant during the play and in the rambles of the boys of 
one or more families. This "boy-leader," or pedagogue, 
was usually a Greek; only he was not, by right of birth, 
invested with citizensliip. He was a serf, owned by tlie 
state and assigned to service to free-born citizens; but, 
being attached to the soil, he could not be sold. 

It was the duty of the pedagogue to supervise the play of 
the boys committed to his care, and to give them such 
mstruction as was then deemed important. His special 
duty, which was not to be neglected, was to attend to 
the development and training of the physical powers of 
his charge; for the possession of a healthy, strong, and 

§ 1 



2 PEDAGOGICS OF ARITHMETIC. § 1 

symmetrical body was regarded as far more desirable than 
a well disciplined mind. 

3. Distinction Between "Art" and "Science." 

The terms art and science are much used as the near equiv- 
alents, respectively, oi practice and theory — art and practice 
having reference to doing, science and theory to the rules 
that regulate actual performance. Thus, a man may be 
quite expert in the art or practice of argument or disputa- 
tion, and yet know nothing of the science of logic, by the 
principles of which correct argument must proceed. Again, 
one may be a fine performer in music, and be ignorant of 
the science or theory of the subject; or he may know the 
theory very thoroughly without having any skill in the art. 

At the time when the pedagogue plied his vocation in 
Greece, pedagogics was only an art. No code of principles 
had been formulated by which his work might be regulated 
and its defects criticized and corrected. His method might 
be skilful and highly successful, but his choice of means was 
a matter of instinct or judgment and not in accordance with 
an organized science of teaching. 

Since that far-off time, teaching, like nearly every other 
practical matter, has developed into a science. The nature 
of the child, the order in which his faculties develop, and the 
laws in accordance with which those faculties operate, the 
suitability of certain subjects as training matter for certain 
faculties: these, and many other facts and conditions have 
been investigated and discussed, until now one may learn 
many of the principles upon which success in teaching 
depends before he enters upon the actual work in the class- 
room. In other words, teaching is not only an art, but it is 
also, in a very satisfactory sense, a science. Hence, we may 
write the following 

Definition. — Pediig:og-ics is the science that treats of the 
principles and t lie methods of teaching. 

3. Pedagogics of Avitliinetic. — It follows from what 
is said above that the pedagogics of arithmetic is that divi- 
sion of the general subject of pedagogics that has reference 



§ 1 PEDAGOGICvS OF ARITHMETIC. 3 

to the teachini^- of arithmetic. There is a general impression 
abroad that ahnost anybody can teach aritlimetic success- 
fully, provided he understands it. That this is not the case 
is proven by the fact that the beginner, without professional 
training, is almost inevitably vmskilful, however thorough 
may be his knowledge of mathematics. He does not know 
how to begin or where. He cannot get down to the level of 
his pupils, for he is misled by the fallacious notion that what 
seems so easy and clear to him must be equally so to the 
children he wishes to instruct. After long experiment and 
many failures he learns that not even high scholarship will 
insure him the success he courts. At first he attributes his 
poor results to the stupidity of his pupils. He never met 
children quite so dull, he thinks, and tells of it at home, 
perhaps, as an unaccountable fact peculiar to that one 
locality. 

But some fine day the principal, the superintendent, or 
some other experienced teacher comes in and gives him a 
shock by showing him that the pupils he thought so slow 
and stupid are capable of being aroused to the most eager 
attention and interest. He finds himself wondering how it 
was done, and remembers having heard somewhere that 
special training over and above mere scholarship is requisite 
to success in teaching even so simple a matter as arithmetic. 
He begins to believe that teaching is really a science as well 
as an art, and that he has missed one of its important divi- 
.sions — the pedagogics of arithmetic. 

4. i:)ivisions of Aritlunetic-al Study. — The study of 
arithmetic is more or less distinctly divided into three 
periods : 

1. Primary Aritliutclic. — This period is generally esti- 
mated as covering about four j-ears. The work consists in 
learning very thoroughly all the fundamental combinations 
of integers, including numeration, notation, the four fiuida- 
mental rules, operations with the most commonly iised 
denominate numbers, simple exercises in fractions, and 
many practical examples involving not more than two 



4 PEDAGOGICS OF ARITHMETIC. § 1 

operations. The leading objects to be attained during this 
period are rapidit}^, accuracy, and thoroughness. 

2. Intermediate or Elementary Arithmetic . — This period 
should include a very thorough review of the primary work 
with larger numbers and new applications. In addition to 
this, properties of numbers, common and decimal fractions, 
denominate numbers, with areas and volumes, and many 
practical problems, should follow. The time should be about 
two years. 

o. Advanced ^Iritltmciic. — A review of preceding work 
.should be followed by percentage and its various applica- 
tions without and with the element of time, proportion and 
its applications, powers, roots, mensuration, and the metric 
system. The neces.sary time to do this work well is about 
two school years of forty weeks each. 

5. Primary Teacliiii^' tlie Most DifUciilt. — The longer 
a course in arithinetic is pursued, the more familiar does the 
teacher become with the needs and capacities of the pupils. 
It is the beginning that is difficult. When, at the age of 
about six years, the little ones appear in school for the first 
time, their minds are very nearly a blank with respect to 
numbers. They all know what is meant by one and two, but 
few of them have a suiffcient acquaintance with three and 
four. Some of them, indeed, have learned to count, perhaps, 
as far as ten, but this really goes for little. To know auto- 
matically — without thought or hesitation — the arithmetic of 
the fundamental numbers is what is required, and of this 
kno:^dedge they have nothing. Not one of them, perhaps, 
can tell the sum of two and three, or how many twos there 
are in four. 

The fir.st discovery that the teacher will make, — and a dis- 
heartening one it is, — is that these children have no power 
of voluntary attention. Their eyes wander about in search 
of something novel, and a certain want of fixity in the eyes 
exactly denotes the nature of the mind's action. If the atten- 
tion of a few of them is gained for a moment, it lapses again 
almost immediately. It is impossible to hold their united 



§ 1 PEDAGOGICvS OF ARITHMETIC. 5 

attention steadily on one subjeet for longer than even a sing-le 
minute. Skilful indeed must be the teaeher that can carry 
them all forward along the path of knowledge without pause, 
miscalculation, or blunder. In all the range of a teacher's 
work there is nothing so difficult as this earliest task — to 
make a proper beginning. 

Obviously, it is of great importance that the teacher shall 
know very definitely and thoroughly what this earliest Avork 
should consist of, how it should be begun, and how it should 
be conducted during the first school years. And the fact is 
that this is precisely what the young teacher does not know. 
It is one of those matters apparently so easy as to require no 
kind of preparation, while in reality it should have the most 
elaborate and thorough attention beforehand. The popular 
misconception that this first work is one of extreme sim- 
plicity — one that any one can do — suggests an anecdote that; is 
related of the great painter Hogarth. 

A father approached the artist with a request for a place 
in tjie studio for his son, who had an aptitude for drawing. 

"What can he do ? " inquired the artist. 

"Well, I thought you might find him useful at first in 
painting the backgrounds for your portraits, and easy work 
of that kind," answered the father. 

"If he can paint backgrounds, he is just the person I 
want," replied Hogarth. "I have spent many years trying 
to learn how to paint a background for a picture, and I am 
not yet able to do it well." 

G. Selienies for Karliest Work in Aritliiiietie. — As 

might be expected, many educators have recognized the dif- 
ficulty of a proper beginning in number work, and have 
wrought (Hit very elaborate plans intended to be complete 
both in method and matter. One of the most celebrated of 
these is the Pestalozzian System of Primary Arithmetic. It 
is not in accordance with our present purpose to explain its 
details in this work. The system was at one time very popu- 
lar, and even yet there are many educators that think it excel- 
lent, which it undor:btedly is; others criticize it on the ground 



(! PEDAGOGICS OF ARITHMETIC. § 1 

that it takes on difficulty with too o-reat rapidity. Whether 
thivS objection is warranted or not, one thing is certain — it 
brought to educators the conviction that a system of some 
kind is essential, and set them to the task of improving upon 
that proposed by Pestalozzi. Many modifications of the 
scheme of this edticator of more than a century ago have 
resulted from the thought and discussion that he induced. 
Among these is the celebrated " Grube Method," first pub- 
lished in Germany in 18-12. Many editions of this work, 
each different in some respect from the preceding ones, have 
appeared since. Whatever may be the plan he decides to 
follow, every teacher should possess copies of it, either trans- 
lated or in the original German; for it is onh^ by knowing 
and considering what others advise that he can hope to find 
that which is best suited to the needs peculiar to the situa- 
tion he is required to meet. 

The Grube method also, like that of Pestalozzi, has been 
severely criticized ; but the student should remember that no 
system of any kind in which there is the slightest chance, for 
difference of opinion has ever been accepted without protest 
and vigoroiis opposition. Indeed, every new departure is only 
a compromise, and, at any moment, is liable to be changed 
for something else. Doubtless, both the S3'stem of Pesta- 
lozzi and the method of Grube are full of faults of omission 
and commission; but the fact must not be forgotten that 
they are sharply defined plans, — well considered methods, — 
and therein is their chief merit; for even a poor plan of pro- 
cedure is incomparably better than no plan at all. The 
methods of the.se educators are almost certain to be better 
than anything the beginner could find out for himself, and to 
study them will set the student to thinking about ways and 
means. They have the effect of making him aware of th.e 
difficulties that await him, which goes a long way in helping 
him to overcome them. 

7. The Plan of This Paper. — It is not intended to 
present the student with a novel plan of teaching arithmetic, 
or to direct him along a royal road to success in his work. 



§ 1 PEDAGOGICS OF ARITHMETIC. 7 

The purpose is to explain clearly and minutely a method 
that has been the outgrowth of long experience under many 
different conditions, and one that sjcms to be suited to the 
requirements of this country and this time better than 
either of the schemes mentioned above. The method is not 
a creation but a growth. Beginning with the Grube method, 
a good many years ago, the writer has watched its working 
in the hands of a great many teachers of every degree of skill 
and ability. He has heard their criticisms and objections 
with respect to this and that feature, and he l)clieves that 
many advantageous changes have from time to time been 
made. Much that was done for no definite future advantage, 
much that was merely mechanical, has been omitted or modi- 
fied. Additions, too, have been made. vSome of these addi- 
tions were owing to the conceded fact that the study of 
arithmetic should be for three distinct purposes; nameh': 

(a) Mental discipliiic. 

{b) Preparation for later and //i^-^'/ier niatlieniatieal work. 

(r) Practieal nsefnlness. 

Now, it is well known that in this country any scheme not 
distinctly utilitarian is looked upon with disfavor. Of 
course, we all admit the great value of mental discipline for 
its own sake, biU educators in this country have discovered 
that this end may be attained just as well — much better, 
indeed — when the primary object is practical usefulness. 
Hence, we have a generally recognized principle of peda- 
gogics : 

N^o snbjeet nnist be admitted to the sehool enrrienlnni unless 
it presents the donble elainj of diseipline and utility. vSo that 
all those arithmetical drills and exercises that were so com- 
mon in the schools and textbooks a score of years ago are 
omitted if they have no promise of ulterior usefulness. 

8. Exercises in Fractions. — An impression is generally 
prevalent that the subject of fractions is much more difficult 
than that of integers. Even many teachers believe this, and 
the consequence is that no subject is so poorly taught as frac- 
tions. They are not taken up until after the pupil has been in 



8 PEDAGOGICS OF ARITHMETIC. § 1 

school for several years, and then they are treated by arbi- 
trary mechanical processes rather than by analysis, as 
integers are. But in these days when analogies, relations, 
and correlations are constantly engaging the attention of 
educators, it seems natural and necessary to bring out the 
fundamental likeness between integers and fractions, and to 
emphasize the fact that the same lines of analysis that are 
applicable to the one are equally so to the other. Every 
thoughtful teacher knows that a fractional imit is as really a 
imit as that which measures an integral number. That is to 
say, a fourth of a dollar is as much a i:nit as the dollar itself. 
Indeed, there are very few absolute units. Nearly every- 
thing' is a part of something else, but nearly every part may 
be treated as a unit. One of the most serious difficulties 
with beginners comes from the failure to recognize the 
analogy between integers and fractions. Only after years of 
work in arithmetic is the discovery made that tlie same 
reasoning by which difficulties are resolved with integers is 
available for the difficulties in fractions. The likeness 
between such examples as the f (^11 owing is not discovered 
until a late day in the history of arithmetical study, and very 
frequently not at all: 

ExAMi'i.K. — If 2 oranges cost 4 cents, how much must be paid for 
3 oranges ? 

ExAMi'LE. — If 5 of a yard of ribbon cost | of a dollar, what must be 
paid for | of a ^-ard ? 

It is believed to be best, therefore, to begin the work with 
fractions and integers at the same time, and to carry them 
on side by side during the first four years, or longer, of 
number work. There is nothing intrinsically difficult about 
thirds or fo!i7'ths any more than there is about three or four. 
It is the notation of fractions that makes them appear differ- 
ent from integers and harder to imderstand. When spoken, 
one-fifth is just as simple as fii'e, and t7vo-tJiirds is as easy 
for the child to grasp as txvo threes. It is when written 
i, I that they seem difficult, but in reality they are not; 
for I does not express a compound idea any more than t%oo- 
tliirds or tzvo apples. In brief, the alleged complexity of the 



§ 1 PEDAGOGICS OF ARITHMETIC. 9 

subject of fractions is largely imaginary, and arises from the 
fact that until lately their consideration has been deferred 
until the fundamental rules with integers, United States 
money, the properties of numbers, divisors, multiples, and 
cancelation have been mastered. Then they are taken up 
and learned only so far as mechanical processes are con- 
cerned. Their correlation with integral numbers is systemat- 
ically overlooked; the student, and usually the teacher also, 
never suspects that three fourths and three apples are in 
reality concrete integers, and recpiire in problems exactly 
the same analytic treatment. The teacher having been 
badly taught himself, therefore, and having failed to master 
fractions properly and to learn the analogies between frac- 
tions and integers, proceeds to teach as he was taught and to 
leave obscure that which is essentially simple. 

9. Drill Work. — Very little doubt can be entertained 
about the extreme utility of systematic and persistent drill 
work in the early part of the course in arithmetic. If, while 
reading, it is necessary for a child to stop frequently in 
order to spell and puzzle over words, it is impossible for him 
to get the meaning of what he reads. The case is similar in 
arithmetic. If the student must let go the main thread of 
an analysis or operation in order to consider how much the 
sum or the product of eight and seven, or some such combi- 
nation is, he is almost sure to be unable to resume when the 
uncertainty has been settled. Indeed, the one essential and 
indispensable object to be attained in this fundamental work 
with children is infallible accuracy and extreme ease and 
rapidity. In other words, the "divine last touch" in educa- 
tion is automatism — the facility by means of which a task 
that was before slow, laborious, and painful, seems, by some 
innate principle of activity and intelligence, to work out its 
own results; or, as we say, to "do itself." The writer, on 
one occasion, noticed a clerk in a large wholesale establish- 
ment add up very long columns of figures almost at a glance. 
The speed was so extreme that one could scarcely conceive 
a mind capable of being so trained, or believe that the result 



10 PEDAGOGICS OF ARITHMETIC. § 1 

was correct. When asked to explain the mental process, the 
clerk professed himself unable to do so. 

" I just run my eye along the column and I seem to know 
the result without any distinct sense of intermediate steps. 
It is very much like intuition, which is a kind of argument 
so rapid that the successive steps leading to the conclusion 
are not noted or remembered." Something like the fore- 
going was what he said. This is very nearly an example of 
automatism ; very much like~ what we do when we read — we 
follow the thought, giving no conscious attention to the words 
that express the thought. 

This automatic facility is what the teacher of arithmetic 
should aim to give the children under his care ; for, as long 
as their attention is diverted from the reasoning necessary 
to the solution of a problem to the mechanical operations 
involved, so long will they be lacking in confidence, and so 
long will they be uncertain in results. This mechanical part 
of the work must be like that done by a perfect machine 
that runs without friction or noise. 

Now this ease and rapidity, this automatism, is attainable 
only by incessant practice with suitable drill work. The 
clerk that, finally, is able to get his resiilts by a process 
almost as rapid as intuition, and to be so certain that he may 
neglect all possibility of error, must pay the price of years 
of practice. In like manner, the teacher that would secure 
a similar proficiency on the part of his pupils, in the inere 
routine of arithmetic, — in its viccJianics, — must work for it, 
and work very hard. And the end is a full equivalent for 
the Igjjor it costs. 

10. No Drill Witliout a Purpose. — In the textbooks 
on arithmetic that were used in our schools three or four 
■decades ago, there were a great many exercises that had no 
conceivable bearing upon any of the number work that was 
to follow, either in the book itself or in the actual life that 
was to come after the school. If they had any definite pur- 
pose to fill, it was not obvious. Certainly nothing beyond^ 
mere discipline was aimed at, and, as we have seen, this in 



§ 1 PEDAGOGICS OF ARITHMETIC. 11 

itself is no longer much sought after. vSome examples will 
illustrate what is meant. 

1. Add by 2's from to 100; by 3's from to 99; by 3's 
from 1 to 100; by 7's from 2 to 100. 

2. Begin at 100 and subtract by 3's until the last remain- 
der is less than 3. 

No such addition or subtraction is ever required in solving 
any example, nor is it in any way a preparation for any prob- 
able demand of the future. Much of such work that is utterly 
witliout definite object or purpose is done in our schools in 
connection with nearly every subject in the curriculum. This 
is a fault that is very hurtful. It mystifies the pupils and 
leads nowhere. It breaks the continuity of any plan the 
teacher may have made, inasmuch as it cannot be part of 
any plan. The teacher should see to it that he works in 
straight lines, and that everything he does shall contribrite 
towards giving his work symmetry and completeness. There 
should be much drill work. In this way he should emphasize 
what he has done during the day, and should connect it with 
what has been done before. But before any exercise of this 
kind is accepted and practiced, let him clearly decide about 
its purpose and utility. "Is it exactly what I want? Just 
what do I require, and why do I require it ? Is it possible 
for me to find soinething or devise something that will better 
meet my purpose ?" 

And, then, when he has found a useful drill or device of any 
kind, let him copy it into his note book for future use. These 
plans can be obtained from many sources. They can be 
found in textbooks, in educational publications, and they 
may be learned from other teachers, but many of the best of 
them for his purpose will arise from the exigencies of his 
own work. Whatever be their source, they should be copied 
in proper order in his note book, and should be accompanied 
by such explanations of their purpose and the manner of 
using them as will make them readily available for future use. 

^X^l 1. Concrete Appliances. — There is a great variety of 
opinion about the extent to which objects should be used in 



12 PEDAGOGICvS OF ARITHMETIC. § 1 

early number work, and at what stage they should be laid 
aside and the work with abstract numbers begun. For 
example, one author says: 

"For a successful teaching of number, the teacher needs 
a great variety of objects. Blocks, splints, sticks, buttons, 
paper patterns, peas, beans, corn, spools, counters, shells, 
pebbles, horse chestnuts, acorns, little tin plates, cups and 
saucers, tin money, are inexpensive and convenient to handle. 
For measurements, the teacher must have inch measures, 
foot rules, yard measures, a set of tin measures, a set of 
wooden or pasteboard measures, a set of weights, and a pair 
of scales." 

This abundance of material requires a place where the 
many objects may be kept, and an arrangement for quickly 
and quietly giving them out and collecting them; and, 
besides, some means must be provided that they may be 
handled by the children without confusion. All this involves 
a great outlay of time, and the abiindance of illustrative 
material may become an obstacle instead of a help, by 
diverting the attention of the children from the real busi- 
ness in hand. The author quoted above has evidently 
thought of the difficulties attending this matter, but just as 
evidently he has never been situated where he was required 
to do the actual work, for in another place he observes: 

"It is more convenient in these exercises to have the 
children stand about a table on which are the objects to be 
handled. Let them illustrate each story ( ? ) with objects 
until it is evident that the relation between the numbers is 
as clearly seen without the objects as with them. " 

Without meaning to do so, this author, in another 
place, formulates what amounts to a serious comment in 
objection to the embarrassment of concrete richness advised 
above. 

" Whenever a tnental picture is formed," he says, "then 
the material is a hindrance to the teaching. Objects are a 
means to an end, but not the end. When an idea has been 
abstracted from the concrete, objects no longer have an 
office to perform and should be put aside." 



§ 1 PEDAGOGICS OF ARITHMETIC. 13 

l*-i. Other A'ieAvs on the Use of the Concrete. 

Another writer on the subject of teaching arithmetic advises 
against the use of many objects, on the ground that a multi- 
plicity of objects, colors, and forms attracts the attention of 
the children from the Jiitmbcr to the objects i:sed in teaching 
it. He recommends that only splints and marks made on 
the blackboard be used, and says that the splints should be 
dispensed with just as soon as the children can use lines on 
the blackboard for counters, and that the lines are unneces- 
sary after children have reached the point where they can 
illustrate by imaginary counters. He enunciates in the fol- 
lowing an important principle: "Never use apparatus for 
the sake of using it. Use it only when it is really needed to 
give a clearer conception of a truth, or when an unsatis- 
factory result would follow without it." This is exactly the 
theory of Pestalozzi; and many other writers on education 
agree in the opinion. 

The writer remembers having once yielded to the insist- 
ence of a teacher that believed in using a great variety and 
abundance of concrete material. She asked for long tables 
to lay across the tops of the desks, and for other tables on 
which to place shallow pans, very long and wide, containing 
sand. Her plan was to have the children surround these 
tables, which were covered with small objects of many kinds. 
These were to be used by the pupils in illustrating various 
operations in number, and they were to be used in concert, 
following the lesson as it was developed point by point by 
the teacher. It was quickly apparent that the objects 
absorbed the entire attention, and the numbens — the lesson 
— was only an annoying interruption of the childish delight 
that the toys, considered merely as playthings, would have 
furnished. With these alone they could have been completely 
happy, but not entirely so with the superadded attempt to 
make their toys a text for a lesson in number. 

Complaints from the janitor then began to reach the prin- 
cipal. The tables, he complained, were in the way, so that 
he was unable to sweep satisfactorily; the furniture could 
not be dusted properly, objects were piled up in disorder 



14 PEDAGOGICS OF ARITHMETIC. § 1 

in every available place, and were constantly falling or 
being knocked down. ' ' I wonder what they are all used 
for," he said; but upon being assured that the teacher was 
"conducting an experiment in pedagogics," he readily 
resigned himself to it for a time, a victim for the sake of 
scientific discovery. 

13, The Experiment. — The principal was very much 
interested in the result of the experiment, and encouraged 
the teacher to make the most of it. She was really a very 
intelligent lady, wrote innumerable articles for educational 
publications, and read very extensively on the subject of 
teaching. And she persisted in a surprising fashion, for she 
had written much on the use of objects in primary teaching, 
and thoroughly believed in what she had written. It was 
quickly apparent that much time was consumed in getting 
ready for lessons, and, after the lesson was finished, in 
removing the material that she had been using; for it was 
impossible to get the attention of the pupils to any other 
lesson as long as those lovely "playthings" could be reached 
or even seen. Then, too, she made some discoveries about 
the proneness to evil — the total depravity — of " those little 
wretches." She found that they were carrying away her 
precious material — abstracting her concrete, so to speak. 
And some of the boys would slyly throw corn, nuts, acorns, 
horse chestnuts, and other missiles at one another. One 
boy, with an instinct for experiment, inserted a bean in one 
of his ears. The incident broke in upon the continuity of 
the work during the rest of that day's session and made the 
services of a surgeon necessary. The teacher paid the bill. 
To add to the realistic effect of the objective method, they 
purloined and ate her oranges and apples, and tried to eat 
some other things that would not have tempted the appetite 
of an ostrich. She reported these doings to the principal, 
but he was unable to help her further than to quote, " Lead 
us not into temptation." The story of that experiment 
would be, if fully told, a very long one; but the results 
accomplished could be told in one word — failure. In an 



§ 1 PEDAGOGICS OF ARITHMETIC. 15 

adjoining room was another class of the same size and grade. 
The teacher of that class also believed in the utility of the 
concrete in those earliest lessons, but she used only splints, 
and illustrations of the simplest kinds on the blackboard. 
At the end of the first half year she had carried her class 
very far beyond the point reached by the other. Fvirther 
experiment was given up, and the business of real teaching 
was resumed. Some bushels of educational illustrative 
material were used to gladden the heart of the janitor. Some 
of it he fed to his chickens, and the remainder he called, in his 
vulgar way, trash, and burned it in the school furnaces. 

14, Ijejyitimate Use of Ajipavatiis for Illustration. 

Lest the writer may be misunderstood on this subject, an 
explanation seems to be necessary. Some kind of objective 
representation is absolutely indispensable in primary teach- 
ing, and the earlier the teaching is begun the greater should 
be the abundance and variety of objects required. The con- 
scious life of a child begins with the knowledge, acquired 
through the senses, of external objects. He thinks almost 
not at all ; he merely perceives a vast number of things and 
some of their most conspicuous equalities; he notes very 
slightly their differences and resemblances; and he begins 
to learn their names. To him nothing is very real except, 
the sensible objects around him. Sense perception is all 
and in all. 

He goes to the kindergarten. There he continues to see 
and to hear, and to observe the realities that make up his daily 
surroundings; only he does it no longer at random. Method 
is introduced, and plans are found to arrest and hold his 
attention more steadily, in order that he may observe more 
closely. Differences and resemblances are emphasized, and 
he is taught to use in easy ways the faculties of judgment 
and comparison. So far he has not been required to deal in 
any manner with abstractions. Everything that he does 
relates immediately to the concrete, and his chief business 
is to acquire a vocabulary. The noun, the adjective, and, to 
a slight degree, the verb, are the parts of speech he learns. 



16 PEDAGOGICvS OF ARITHMETIC. § 1 

This is where the concrete, and nothing but the concrete, 
should be found. There need be no fear that the variety of 
objects, their striking colors, or other qualities will divert 
his attention from something more important. 

He leaves this place of the concrete and enters the ordi- 
nary school region — the domain of the abstract. He carries 
with him, of course, his instinct and liking for the object — 
the reality. But however hard he may find it, he must 
learn to go alone — must learn to supply an imaginary object. 
But the transition must not be too abrupt. Some few, but 
very few, of the old objects may remain with him for a time. 
They must not, however, be very striking, for they are not 
the chief concern in his new work. They are only means to 
an end — stepping stones, by the help of which he may con- 
ceive of the abstract. Grube advises the use of simple marks 
on a blackboard, and these are perhaps all that are really 
required. The splints that are sold in bundles of a hundred 
are very useful, being easy to handle, and without any inter- 
est whatever except as counters; and, although they con- 
sume little time in handling, they should be used less and 
less, and should be given up as soon as possible — not earlier, 
however, than at the end of the first year. 

So that, while it is a principle in pedagogics that we must 
proceed from the simple to the complex, from the particular 
to the general, from the concrete to the abstract, it is equally 
a principle that the ultimate object to be sought in educa- 
tion is independence and divorcement from the sensible, 
the objective, and ease and facility with the abstract, the 
pure ideal. 

15. The Blaclvboai'd in Teacliing. — While a multi- 
plicity of objects is likely to be hurtful in teaching, their 
representation on a blackboard is highly advantageous and 
helpful. Made by means of a crayon, they serve the pur- 
pose of counters admirably in teaching arithmetic; and, 
since they do not interfere with the continuity of attention 
on the part of the pupils, they are much better than the 
reality they represent. Every kind of object may be rudely 



§ 1 PEDAGOGICS OF ARITHMETIC. 17 

indicated. No teacher needs to be expert with crayon in 
order to use it for ilhistrative purposes; indeed, the writer 
has hstened to tlie most intensely interesting lessons con- 
ceivable, illustrated at every point with crayon sketches, and 
at the end of the exercise, a person that had not heard it 
would not, by any chance, imagine that the multitude of 
apparently meaningless marks covering the blackboard had 
been used to aid in anything that had unity and continuity. 

It is easy to spoil a lesson by having too many objects, but 
no such danger can come from using too much crayon. It 
would not be easy, indeed, to put too much blackboard sur- 
face into a classroom. Many of the matters taught from 
day to day can be put in some unused place and frequently 
reviewed. When it is desired to call special attention to 
anything it may be written with colored crayon. There is 
much that might be said on the subject of colored crayon 
and its great helpfulness in teaching little children, btit this 
is scarcely necessary, for it is now known and used by nearly 
every teacher. 

16. Grainniai* of Aritliinetical liaiigrnage. — The 

teacher will hear frequent discussions concerning the gram- 
matical correctness of certain expressions that he is com- 
pelled to use almost constantly in teaching arithmetic. For 
example, should we say, "One and one is two," or "One 
and one a?'e two" ; " Twice three w six, " or " Twice three 
are six"; "Eight and seven is fifteen," or "Eight and 
seven ai'e fifteen "; "If five dollars is one-half of my money, 
etc."; or " If five dollars a?-i' one-half of my money, etc."; 
" Two- thirds of six is four," or "Two-thirds of six arc 
four"? If there is a right way, the teacher should know 
what it is and follow it steadily. The textbooks illustrate 
the most varied usage in the matter, and it would, perhaps, 
be impossible to find two writers on arithmetic that agree 
throughout in this respect, or one that is always consistent 
in his own works. 

One book now before me contains, amongst many other 
bewildering constructions, the followinu": "One time one 



18 PEDAGOGICS OF ARITHMETIC. § 1 

ts one," "Two times one are two," "How many t's three 
times two?" "Two arc contained in eight four times," 
"Two and one is three," "Two and two arc four." 

A certain grammarian says, "In multiplying ojic only, it 
is evidently best to use a singular verb; as, 'Twice one h 
two.' (He advises also, ' Twice naught ?> naught. ') And, 
in multiplying any number above our, I judge a plural verb 
to be necessary; as, ' Twice tico arc four.' " 

Goold Brown, in his ' ' Grammar of English Grammars, " 
argues this matter at great length and quotes all kinds of 
contradictory usages and opinions, but seems to be somewhat 
uncertain himself, although he disctisses with much heat and 
apparent intolerance the opinions of Dr. Bullion and some 
other writers. The teacher would do well to examine Brown's 
presentation of the subject (see pages 584: to 592 of his 
work) . 

Now, this whole question is resolved if it can be decided 
just what is to be regarded as the subject of the verb. Con- 
sider the following sentences, the correctness of which no 
grammarians dispute: 

"All work and no play viakcs Jack a dull boy." 

"Little and oiten Ji//s the purse." 

" Bread and butter is the staff of life. 

"The long and the short of the matter is, etc." 

"Five dollars taas too much by far." 

Matthew Arnold writes, "The power and value of Eng- 
lish literature Zi>as thereby impaired." 

And the following is one of many examples that may be 
found in Macaulay: "All the furniture, the stock of shops, 
the machinery which could be found in the realm zuas of less 
value. " 

In all these sentences the apparently compoiind subject is 
made up of elements that must be taken together to make a 
complete singular whole. Thus, when we say, " Bread and 
butter is the staff of life," we do not mean that bread alone, 
or butter by itself, is the'staff of life. The sense is that the 
combination of bread and butter — bread zvith butter on it — 
is the staff of life. So, when we say, " Eight and seven is 



§ 1 PEDAGOGICvS OP^ ARITHMETIC. 19 

fifteen," we do not mean that cigJit is fiftcoi or seven is 
fifteen; it is their combination into a single aggregate of 
which we are thinking. 

Dr. Bain, in discussing this subject of the concord of the 
verb and its subject, gives the following general principle: 
Unless IOC can resolve a plnral construction into a number of 
distinct singular affirmations, the employment of the plural is 
not justified. For example, the plural verb is required in 
the sentence, "John, Peter, and Mary are here," since we 
may separate the expression into three "distinct singular 
affirmations," "John is here," " Peter is here," "Mary is 
here." But it is impossible, without changing the fact, to 
separate in this manner such expressions as, " Six times five 
are thirty," "Three-iiftlis of my money arc nxwe. dollars," 
"Five shillings were the damages," "Five and four are 
nine, etc." Hence, the verbs in these cases should be in the 
singular. 

Dr. Webster, in his " Philosophical Grammar," writing on 
the same subject, remarks: When an aggregate number is 
expressed by the plural names of the particulars composing 
that amount, the verb may be in the singular. Thus, 
"There was a hundred and fifty thousand pounds sterling." 
This is, in other terms, the principle enunciated by Mr. 
Bain. 

In asking questions, the teacher is compelled to use the 
forms "How much" and " How many." Almost every one 
follows the "How much" with a singular verb, as "How 
much is two times six?" " How much is four and five?" 
With "How man}^, " however, the many seems to call atten- 
tion to the number — the count — instead of to the mere mass 
or aggregate; and many teachers will say "How many c?;'c 
three times two ? " According to Dr. Bain's principle, 
however, this is " not justified." It is at least not necessary, 
for we are guilty of no error when we say " How many is 
three-fifths of twenty ? " 

17. Hemarks on the ForejEfoinia: Discussion. — It 

must be said that the usage is well established among the 



20 PEDAGOGICvS OF ARITHMETIC. § 1 

writers on arithmetic of printing' the tables belonging in the 
fundamental rules with plural verbs, or of evading the 
matter altogether by using signs. It is easy to find such 
cases as the following: 1 and ts 1, 1 and 1 a?'e 2; 5 less 4 
is \, 5 less 3 (rre 2; 1 time 2 is 2, 2 times 2 arc 4; 2 a?'c con- 
tained in (j three times, 2 is contained in G three times; 
three 3's are or is nine, etc. 

One thing is pretty certain — whetlaer you use the singular 
or prefer the plural, in either case you can usually find as 
good argument and authority for your preference as any one 
can find against it. The matter is in hopeless confusion, 
and it will probably never be settled in a way to be accepta- 
ble to everybody; for argument on the subject never leads to 
any valuable conclusion. Believing that a teacher's language 
should be at least consistent from day to day and from sub- 
ject to subject, the writer would advise the student to decide 
upon one usage or the other, and then practice that alone 
and require his pupils to do the same. Whatever your choice 
may be, some one will say that you are in error; that, how- 
ever, makes but little difference. The important thing is to 
have reasons for what you do, and to be steadily of the 
same mind and practice, unless you discover that you are 
imdoubtedly wrong. 

The writer's preference is for the singular verb. The 
reason for this is that you do not have to abandon the singu- 
lar in certain cases and use the plural. But if you decide in 
favor of the plural verb, you are compelled very often to use 
the singular; as, for example, i i such sentences as the fol- 
lowing, in which it would be extremely difficult to justify 
the plural verb: 

" The sum of 'S and 4 is l." " Five less 3 ?s 3." " Six taken from 
10 leaves 4." '■ Ten divided by 2 gives 5." " Three is contained in 
12 four times." "The half of 6 is 3." " Six is 4 more than 2." Etc. 

18. The Use of Sig:ns. — Some writers urge that the 
symbols for addition, subtraction, multiplication, division, 
and equality should not be introduced to the pupil until after 
he has been taught in number for several months. This is, 



§ 1 PEDAGOGICS OF ARITHMETIC. 21 

however, a needless precaution. The pupil able to under- 
stand the significance of and will just as readily understand 
its briefer form, +• Indeed, the latter is more vivid in 
effect, for the child quickly discovers that besides denoting- 
mere aggregation, it is a symbol of operation — it is the 
equivalent of a verb in the imperative mood. It says to him 
very distinctly, "Add the.se numbers together." The sign + 
indicates nothing that is not easily within the comprehension 
of the youngest pupil, and the sooner it is thoroughly under- 
stood the better. Symbols are, in general, more exactly 
significant, and the mental effect they produce is stronger 
than the significance or eft'ect of any mere verbal equiva- 
lent or approximation. Hence, when the idea of any opera- 
tion or relation is to be taught, then is the time to introduce 
the symbol, if there be one. And then, this work should be 
done thoroughly; for if there is any vagueness among the 
pupils with respect to the meaning of a symbol, the confi- 
dence so necessary to real progress will be lacking. 

19. Conditions Exiiressed by Symbols. — It is not 

enough that the children should know what operation or 
relation is denoted by the signs used in arithmetic. Some 
of the most delightful exercises may be had with them from 
the very first. One of the most excellent teachers of little 
children that the writer has ever seen at work was the first 
to suggest to him the possibilities in this direction. These 
exercises she made to include training, not only in the mean- 
ing of symbols, — -the operations and the relations denoted by 
them, — but also in language and in rudimentary reasoning. 
For example, she would write on the board, say, the 
following : 

2-f 3 = 5. 

"Now, Eddy," she would say, "tell me what that says?" 
" It says that two and three more is five." 
"That's right, Eddy; can you tell that in another way?" 
"Yes, ma'am; two added to three makes five." 
" Very well done. Now, can Johnny read it in any other 
ways ? " 



22 PEDAGOGICS OF ARITHMETIC. § 1 

Johnny rises and says, "Two and three is five," or "The 
sum of two and three is five." 

" Now, Harry, you tell us in the hard way — the arithmetic 
way," 

Harry follows with " Two plus three is (or equals) five." 

After a time they will know exactly what is meant by all 
the various symbols and will read them correctly. The 
greatest difficulty will be found with multiplication and 
division; especially with division, for the expressions "is 
contained in" and "divided by" are hard for young chil- 
dren, and these expressions have no constant equivalents. 

While, for the sake of getting the exact meaning, it is at 
first necessary to employ various equivalent expressions, 
sooner or later there should be a settling down to a uniform 
technical brevity. The following will illustrate : 

2 + 5 — 3 = 4. " Two plus five inimts three equals four. " 

4 X 2 + 1 = 9. " Four times two, plus one equals nine." 

8 — 3x2 = 2. " Eight, minus three times two equals two." 

6 X i = 3. •' Six times one-half equals three." 

1X8 = 4. " One-half of eight equals four." 

6-7-2 + 8-7-4 = 5. " Si.x; divided by two, plus eight divided by four 
equals five." 

iX6-fjOf8 = 4. "One-third of si.x, plus one-fourth of eight 
equals four." 

20. " Telling: Stories '■• in Aritlmietic. — The work 
indicated above is important, and, if it be done by a very 
skilful teacher, it may be made pleasing to the children in a 
very high degree. But it is by the exercise that is known 
among teachers as "telling stories" in numbers, that the 
highest interest and delight may be aroused. A brief illus- 
tration will make clear w^hat is meant. 

The teacher puts on the board, let us suppose, 

4-3 + 5 = ? 

She then asks, * ' Who can tell me a story about what I have 
written on the board ? " The hands go up all over the room. 

" Mary, you may tell the story." 

"I had four cents, and spent three cents for candy; my 



§ 1 PEDAGOGICS OF ARITHMETIC. 23 

papa then gave me five cents more. How much money did 
I have then ? Answer, six cents. " 

"That's very good," the teacher says. "Now we'll hear 
Annie's story." 

Annie says, "A girl picked four quarts of berries and 
spilled three quarts of them. Then she picked five more 
quarts. How many quarts did she have at the end ? 
Answer, six c|uarts. " 

After one or two more "stories," the teacher puts on the 
board another test for the exercise. The child here is 
deriving profit in several distinct respects: 

1. He is learning the meaning of the signs. 

2. He is performing indicated operations, and thus getting 
discipline in combining" numbers. 

3. His invention is being trained. He goes to his store 
of experience for a situation answering a certain description. 

4. He is formulating the conditions in ordinary language. 
Of course this work can be made of any degree of difficulty; 

but it is not necessary to remind the teacher that if it be too 
severe all interest, as well as all profit, will be destroyed. 
Every lesson should be in some respect different from pre- 
ceding lessons, and it is by such devices that the teacher of 
high skill diversifies her work and keeps alive the interest 
and attention of the pupils. 

31. Types of Examples. — Closely allied to the fore- 
going is the indicating of operations by general symbols 
both of operation and quantity. This is, however, not a 
matter for the pupil, but for the teacher. Every teacher 
should have a note book in which to keep a fund of sugges- 
tions, plans, devices, drills, etc. Now, instead of writing 
down a great number of examples in the hope of getting all 
the useful varieties, it is possible to condense them into a 
few types expressed in general symbols. Thus, suppose we 
have the following examples: 

1. If 1 orange cost 5 cents, how much will 3 oranges cost ? 

2. If 3 oranges cost 15 cents, what will 1 orange cost ? 

3. At 5 cents each, how many oranges can be bought for 15 cents ? 



24 PEDAGOGICS OF ARITHMETIC. § 1 

In these examples there are only three different elements. 

{a) The nui>ibcr of oranges. This may be denoted by ;/. 
(/;) ^\\% price of one orange, or p. 

((•) The cost of all the oranges, or c. 

Now, the operations necessary to the solution of these 
examples, taken in order, may be denoted by the following- 
formulas : 

{a) c = pxii, {b) p = c-^ii, {c) 11 — c^p. 

Each of these formulas represents htmdreds of examples 
that require the same operation to solve them, but they may 
all contain different subject matter. Thus, formula (^r), 
c z=: pxn, may be translated into the following in which no 
allusion is made to oranges or money. 

If a tailor can make a coat in 5 hours, how long will he require to 
make 6 coats ? (Here^ = 5 hours, and n = 6.) 

In one week there are 7 days ; how many days are there in 4 weeks ? 
{p = 1 days, « = 4.) 

Again, introducing an additional operation, we may write 
the following: 

4. If 3 (;/) oranges cost 15 {c) cents, how much {c') will 7 (;;') oranges 
cost ? 

5. If 3 («) oranges cost 15 [c) cents, how many (//') oranges can be 
bought for 35 {c') cents ? 

Expressing the necessary operations by means of formulas, 
we have for (4) and (5), respectively, the following: 

(«r/) c' = c^iixit', {c) n' — c' -^{c ^li). 

As in the case of {a), (/;), and (r), each of these formulas 
represents an immense variety of examples that differ in the 
matters to which they relate, but are alike in requiring the 
same analysis in their solution. Thus, formula (li) may be 
translated into the following among- innumerable other 
examples : 

If in 4 days I can earn $12, how many dollars can I earn in 9 days ? 
A boy can go 24 miles on his bicycle in 3 hours ; at that rate, how far 
can he go in 10 hours ? 

The student will, of course, notice that such formulas are 
available for fractions and decimals as well as for integers. 



§ 1 PEDAGOGICS OF ARITHMETIC. 25 

They are useful, therefore, in every grade of teaching. For 
example, the following are resolved by formula (r), 
n' ■=. c' -^- (r-f- ;/) : 

I pay §9f for | of a ton of hay ; how many tons can I buy for $39 ? 

If a piano is sold for $825, which is 6.'5,'f' of the catalogue price, what 
per cent, of the catalogue price would have been received if it had been 
sold for §875 ? 

The interest of a certain sum of money at Z}S is §21; at what rate 
per cent, would the interest on the same sum be §28.J- ? 

3'^. Usefulness of" Type Formulas. — There are many 
advantages to be gained by the use of formulas that repre- 
sent types of examples. Some of these are the following: 

1 . Tlic Teacher More Easily Works in Straight Lines. — This 
keeping at a thing until it is mastered is a prime necessity, 
and it is a matter in which most teachers fail. Arithmetic 
work is, in general, very desultory and without distinct pur- 
pose. Examples involving the widest differences in princi- 
ple and operation are usvt^lly given during the same lesson. 
The result is that pupils are discouraged and quickly come 
to dislike arithmetic. They are permitted to get no more 
than the merest hint of the logic in a problem when they are 
confronted with an entirely different set of conditions in 
another problem. Examples should be given in series, and 
the examples, while they contain different concrete elements, 
should involve the same analysis — the same logic. Mechani- 
cal difficulties may be slowly increased, but the invoh^ed 
method of solution should remain until it has been perfectly 
mastered. This the type formulas enable the teacher to do, 

2. They Enable the 'Teacher to Secure Unity in J^ariety. 
It was explained in the preceding article that a great vari- 
ety of examples having a constant likeness in principle and 
operation may be made under a given formula. Thus, 
integers, fractions, and decimals; percentage, proportion, and 
interest; partnership, banking, exchange, and mensuration 
may be represented by the same formula. The greatest sim- 
plicity of primarywork and the utmost difficulty required in the 
high school are both wrapped up in these simple expressions. 

3. They Are Extremely Useful in Review Work. — The 



26 PEDAGOGICS OF ARITHMETIC. § 1 

teacher that works by these formulas knows exactly what he 
has done, and is able at any moment to discover whether 
each type has been sufficiently mastered. Instead of review- 
ing each subject by its textbook name, and working" by rule, 
he may review his types, and work by reason. This method 
frees the pupil from the necessity of remembering, and 
teaches him to think. 

Many other advantages from using this plan might be 
pointed out, but it may be assumed that they will readily 
occur to the student as he becomes familiar with it. 

The writer once explained this matter to an examining 
superintendent of schools of one of our largest cities. The 
five formulas given in this paper were explained to him, 
together with the manner of using them. He applied them 
in his official work and professed to think them admirable. 
Some months afterwards he inquired of the writer whether 
these five formulas do not cover every possible example 
in arithmetic. When assured that there are innumerable 
others, he said that he had used them constantly for a long 
time and had never discovered any need for others. They 
can certainly be made very helpful in the classroom. 

23. Advanced AV oi*k AVitli Formulas. — If the teacher 
happens to be an algebraist, he may make many excellent 
applications of formulas in teaching classes in arithmetic 
that are somewhat advanced. Very similar to the " telling 
of arithmetical stories," in primary grades, is the use that 
may be made of formulas in advanced grades. To illustrate, 
let us take the following very simple problem : 

The money ($;«) that I have now, increased by what I can earn in 
10 (a) days at $2i (§<^) a day, will exactly pay for 5 (c) cords of wood at 
.f6|- (^d) a cord. How much money have I now ? 

The steps necessary in the solution of this problem are 
indicated in the formula, 

7U = ex d— axb. 

Hence, the answer is found by substituting in the formula 
the numerical values of the letters. Thus, the money 
m = 5xl6i-10xl2i = 131^-125 = U\. 



§ 1 PEDAGOGICS OF ARITHMETIC. 27 

The task to be required of tlie pupils is to construet 
problems with different numbers and about other matters. 
These problems must require exactly the same operations 
for their solution. The pupils will at first hand in many 
problems that fail to meet the requirements, and the word- 
ing is very likely to he awkward. By persisting, however, 
the needed skill will come. If it seems necessary, the 
teacher may for a time indicate more fully some of the con- 
ditions. He may say, for instance : 

" You may each make an example about a boy that rode 
away from home for a certain distance on a wagon, then con- 
tinued his journey on a bicycle, and finally returned home 
by train." 

Obviously, an exercise like this will furnish discipline in 
many important matters. Not the least important will be 
the expression of exact thought in good English. 

By transposing the equation, 

?/i = cd—ab^ 

we may obtain four other equations in each of which the left 
number is different. Thus, problems are provided for in 
which the answer required is entirely different from that in 
the original formula. Transposing, we have 

, vi-\-ab ni-\-ab cd—vi , cd—iii 

d = : , c = ■ — - — , a = J — , b = 

c d b a 

Having these formulas, the pupils may be required either 
to modify the problems they have already made so as to suit 
the change, or they may make new ones. Suppose that it 
be decided to modify the example at the beginning of this 
article so as to suit the fir.st of the four formulas given above, 

, _ ;// + trb 
c 
It may read as follows: 

With $6;^ and the money I can earn in 10 days at .$2J a day I can paj- 
for 5 cords of hickory wood. What do I pay per cord ? 

Or, taking the formula, 

, cd~ in 

b — ■ 



28 PEDAGOGICS OF ARITHMETIC. § 1 

The example may then read, 

Find my daily wages, if my earnings for 10 days must be increased 
by §6^ in order to pay for 5 cords of wood at $6|^ per cord. 

It may be added that a teacher may use this method with 
great success and yet know nothing whatever about algebra. 
There are, however, very few persons engaged in teaching 
to whom algebra is entirely unknown; and it is doubtful 
whether, without such knowledge, it is possible to teach 
arithmetic with much success. 



FIXDAMEXTAL DKII^LS. 



TUlUAu AVORK FOR ADDITIOX. 

24. Tlie Entl in Tie^v. — It has already been remarked 
that all drill work should have a definite purpose beyond 
mere discipline. Every drill should bring greater mental 
dexterity and aptitude ; but, in addition to this, it should be 
a distinct preparation for some work that must be frequently 
done during life. Now, with respect to addition, what is 
this work ? Clearly, it is to add columns of figures. If one 
wishes to know wdaat he owes his grocer or his butcher, this 
is what he must do; if he becomes a clerk or an accountant 
of any kind, he is constantly called upon to find quickly and 
accurately the footings of columns of figures. Practice 
in addition should, therefore, begin very early, and it should 
bj continued throughout the school life. It is possible not 
to do enough of this kind of work, btit it would not be easy 
to do too much of it. 

Besides the addition of figures in columns, various devices 
may be resorted to in order to increase the inte.est of pupils. 

25. Seliemes for the Blackboard. — Drills like the fol- 
lowing (Fig. 1) may be put on the blackboard in a place where 
they may remain without being in the way. Or, the teacher 
may make suitable charts on large sheets of manila paper; 



1 



PEDAGOGICvS OF ARITHMETIC. 



29 



these, when needed, may be hung np before the pupils, and 
removed when the exercise is finished. 



8 

3 

12 

U 

5 



10 



1 

(") 
11 



+ 2. 3, etc. 




Fig. 1. 



The drill on the left consists in adding 2, 3, etc. to S, 3, l2, 
etc. The pupil should be required to announce results only, 
and as rapidly as possible. 

For the sake of variety, the circle may be used occasionally. 
The exercises may be varied by changing the figure at the 
center. The addition should be from within outwards and 
the reverse, and around the circle both ways, beginning at 
different places. 

The exercise on the right is intended for practice in what 
some one calls decimation — passing by addition from num- 
bers between 20 and 30 to numbers between 30 and 40, etc. 
The figure preceding the plus sign may be changed to 3, 4, 
etc. as the degree of proficiency warrants. The scheme may 
be used in two ways: 

1. The pupil may add each figin'e on the right to 32, 
announcing results only. Thus, 35, 41, 37, etc. 

2. He may add a designated figure on the right to 32, 92, 
52, etc. 

Much added interest is given to such exercises by the judi- 
cious use of colored crayon. 

20, Addition of Colimins. — Every requirement of this 
drill work may be met by the addition of columns upwards 



30 PEDAGOGICS OF ARITHMETIC. § 1 

and downwards, and in both directions from different points 
of beginning. By thus changing the place of beginning and 
the direction in which the addition is made, the intermediate 
numbers touched are in every case different. Ttius, in find- 
ing the sum of the outer circle above, if we begin with 4 
and add in the same direction that the hands of a watch turn, 
the intermediate results will be 13, 15, 20, 29, 35, 37, 44. 
In the other direction, we have 11, 13, 19, 28, 33, 36, 44. 
These are alike only in their final sum, 44. Beginning at 8 
and adding in both directions we have 11, 16, 25, 31, 33, 40, 
44, and 12, 19, 21, 27, 36, 41, 44. 

There are, therefore, always many more orders of adding 
a column, one figure at a time, than there are figures to add. 

In adding a column, the first figure need not be pointed to 
or named: point to the second figure and mention the sum 
that it gives when added to the first. As pupils become 
expert they should be encouraged to omit the pointing. It 
is enough to pass the pointer or a pencil rapidly along the 
column, omitting to mention the intermediate sums. Any 
one that must do these things with laborious precision must 
not expect to add rapidly. Besides, it is a fact that the more 
rapidly an addition is performed, the more likely it is to be 
correct. 

DRILL ^VORK FOR SUBTRACTIOX. 

37. The End to Be Aeconiplislied. — Let us consider* 
what it is that we must do in actual subtraction. Knowing 
this, we shall be able to determine the appropriate drill. 
There are two principal matters that must be effected with 
absolute accuracy, and they should both be done rapidly — 
automatically indeed. These two things are : 

1. To subtract in turn each sub! raJicnd figure from a 
corresponding figure of the minuend. 

2. To ^'■carryf ivJien the conditions require it. 
Omitting for the present the subject of " carrying," we 

may consider the more important matter — the subtracting. 
The subtrahend figure may be any one of the digits from 
to 9, inclusive. When the subtrahend figure is 2, we may 



§1 



PEDAGOGICS OF ARITHMETIC. 



31 



be required to subtract it from any number between and 
including 2 and 11 ; if it is 3 we may have to subtract 3 from 
3, 3 from 4, etc., up to 3 from 12, which last gives a remainder 
of 0. In brief, the subtraction of 
one number from another may 
involve the subtraction of each 
digit from every number that leaves 
a remainder not greater than 9. 
No pupil can be expected to per- 
form the operation of subtraction 
with any certainty as to the result if 
he does not know at once and with- 
out thought all these remainders. 



38. The General Sclienie. 

The general plan of this important 
drill work in subtraction may be 
imderstood almost at a glance from 
the diagram shown in Fig. 2. If 1 
be taken from every number from 
1 to 10, both inclusive, 2 from every 
number from 2 to 11, and so on to 
9 from every number from 9 to 1 8, the 
scheme is complete for subtraction. 

Placed on the blackboard, one at a time, with the minu- 
ends disarranged, to avoid singsong, these drills are as fol- 
lows (Fig. 3) : 




Fig. 3. 



! '^'^ 


3\ 


13\ 

S 




13^ 




8 


- S 




IS 




2 


12 


42 




12 




5 


5 


5 




tr, 




9 
11 


^ 11 


9 
^ 11 


y- — 4, etc. to 


9 

11 


■ ■ 1 
^ -9 \ 


7 
4 


7 

4 


7 
4 




17 
14 


'1 


10 


10 


10 




10 




6. 


G> 


6> 




IG^ 


] 



Fig. 3. 



52 



PEDAGOGICS OF ARITHMETIC. 



§1 



29. Anotlier Drill. — Another exercise of much practi- 
cal value consists in giving- rapidly, at sight, the difference 
between 100 and numbers less than 100, 75 and numbers less 

than 75, etc. The teacher should 
place on the blackboard some- 
thing like Fig. 4 : 

It is a great convenience to be 
able to tell instantly how much 
change one shoiild receive from a 
dollar or a half-dollar after making a purchase. 



100 — 50 — 

A A 


1 75- 


68 


76 




25 


33 


4.-, 


73 


68 




41 


16 


63 


87 


79 


etc. 


17 


24 etc. 



DRII.T. AVORK FOR MFI/riPI.IC ATIOX. 

30. Plan of tlie Drill. — The drills necessary in multi- 
plication are of two kinds: 

1. Those involving the products of elementary numbers 
up to 12 X 12. 

2. Those involving the foregoing products, with the 
additional operation of carrying. 

The multiplication table gives the products of (1), but in 
an order that inevitably results in the much deprecated 
singsong. The teacher is therefore compelled to devise 
some means of avoiding this difficulty. The products indi- 
cated in (1) may be made familiar to the pupil by using the 
brace, as shown in Fig. 5. Nothing but the products should 
be given by the pupils ; and the drill should be continued 
until these products can all be given as rap- 
idly as the child can speak. Even after this 
degree of thoroughness has been attained, 
there shotild be frequent reviews and many 
examples involving the same operation as 
the drill requires. 

When the products by 2 have been thor- 
oughly learned, 3 should be written in its place. 

The examples assigned for solution should 
always be within the limits of the drill work. 
This will make it easy and gradual to learn 
the added operation of carrying. 




PEDAGOGICS OF ARITHMETIC. 



33 



Multiplication with carrying includes two operations : 

1. Recognizing the elementary product. 

2. Uniting with it the number carried. 

These two operations in their best development become 
one. Thus, 7 times 5 increased by 6 is 41, and not 35 + G. 
This is the first point that the teacher should fix. For the 
pupil to say "7 times 5 is 35," and then count G fingers or G 
marks on his slate is bad, and without excuse for the teacher. 
The pupil should, just as soon as possible, say only "41," 
performing both the multiplication and the addition without 
speech. These operations can be performed very much 
faster than they can be spoken. Rapid, involuntary, accu- 
rate mental action is the prime necessity, and for this the 
teacher must labor patiently and persistently. 

In the following exercise (Fig. G), the pupil should annoi:nce 
results only. When the multiplier is 2, and the greatest mul- 
tiplicand 12, no number carried is ever greater than 2 ; when 



3" 
9 

8 
12 

7 


.3^ 
9 
' " ~ ~ S 

« 
12 

yx2^i^ ' 


3A 
9 
5 
S 
12 

^X3+J2 I 


( 1 
y X4 +< etc. 


1 
6 
4 
10 
2> 


1 

6 

4 
10 


6 

4 
10 
2^ 


3 
.4 

■ 

■ 1 



the multiplier is 3, the number carried is never greater than 
3; etc. 



T>RII.L ^VORK FOK DIVISION. 

31. Beveloj)nieiit of the Selienie. — The ordinary 
division table is quickly learned from the multiplication 
table. Indeed, it is an extremely easy inference or deduc- 
tion that if 6 times 7 is 42, then 42 divided by 7 is G, or by 



34 PEDAGOGICS OF ARITHMETIC. § 1 

G is 7. But to know the division table is a very small part 
of what must be known in order to divide rapidly and with- 
out error. Let us examine the following examples: 

5 )38762 6 )59573 7 )183962 

In order to perform the first division we must know the 
quotient and remainder when 5 is divided into 38, 37, 26, and 
12. The respective quotients will be 7, 7, 5, 2, and the 
remainders 3, 2, 1, 2. 

In the next two examples the partial dividends, the quo- 
tients, and the remainders will be, 

59, 55, 17, 53; 9, 9, 2, 8; and 5, 1, 5, 5. 
18, 43, 19, 56, 2; 2, 6, 2, 8, 0; and 4, 1, 5, 0, 2. 

An examination of these results will show just the kind of 
drill work that is necessary in order to prepare for short 
division. 

33. Princiiiles of the Process. — The following facts 
are evident from the foregoing examples: 

(a) The quotient must be obtained one figure at a time. 

(F) Any one of the ten digits may occur in the quotient. 

(c) During the successive steps of the operation, any 
digit of less value than the divisor may occur as a reinainder. 

If we are dividing by 2, the greatest quotient figure 
obtainable is 9, and the greatest possible remainder is 1. 
What number, divided by 2 gives a quotient of 9 and a 
remainder of 1? Evidently, it is 2x9+1, or 19. What 
number, in like inanner, when divided by 3, gives a quotient 
of 9 and a remainder of 2 — a remainder the greatest pos- 
sible ? The answer must be 3 X 9 -|-2, or 29. 

Again, if the divisor is, say 7, in order that the quotient 
and remainder may be the greatest possible, the dividend 
must be 7x9-1- 6, or 69. For a divisor 9, the dividend is 
9x9 4-8 = 89; when 12 is the divisor, the dividend must 
be 12x9 + 11 = 119. 

From all this, it is clear that, before a child can divide by 2 
easily and rapidly, he must know instantly and without 



PEDAGOGICS OF ARITHMETIC. 



35 



reflection what the quotient is, and the remainder also, 
when 2 is divided into any number from to I'J inclusive. 
When the divisor is 3, this knowledge must reach from to 
29 inclusive ; when the divisor is 4, the limits of the drill are 
and 39 ; etc. 



33. General Sclienie. -—The following is a general 
scheme showing this drill in a form suitable for writing in 
the teacher's note book: 











Dividend Jbimits. 










2 
3 


012 


t 
1 


^9, 39, 

i ! 

_J i 


..A9, 

t 
1 

1 

J 


♦ 

1- 
J 


.-_6(>, 


» 


4 






1 
J 






.5 










^ 


(} 














7 
















S 






9 


. . 



etc. 



34. The Scheme in Detail. — For daily use, the divi- 
dends may be written on some unused place on the black- 
board. They should be disarranged as shown in Fig. 8, so 
that no result may furnish a 
clue to the next. The work 
should begin with 2 as a divi- 
sor, and this drill should be 
practiced imtil every pupil is 
expert as far as 10. When 
this has been well mastered, 
the third column of dividends 
may be written and 3 placed 
above as the divisor; and so on 
for all divisors up to 12. The 
pupil should announce results only, and these as briefly and 




3G PEDAGOGICS OF ARITHMETIC. g 1 

rapidly as possible. Thus, in going down the first column 
with 2 as a divisor, all that need be said is 1, 1; 4, 0; 5, 1; 
2, 1; 4, 1; 3, 0; 9, 0; 2, 0; 0, 0; 3, 1. 

This is the longest and by far the most important drill 
work that requires to be done in connection with the funda- 
mental rules. That it should be thoroughly done is indis- 
pensable; for, without it, short division will continue, during 
the entire life of the pupil, to be slow, laborious, and uncer- 
tain of correctness. 

Do not make the lessons so long as to cause the children 
to hate the exercise. Remember that the younger the pupils 
are the shorter should be the lessons. It is impossible 
to hold the attention of very young pupils for a period of 
more than about fifteen minutes, and their early work in 
arithmetic is to them the most difficult and the dullest work 
that they have ever luidertaken. In several of our large 
cities rules have been made limiting all exercises in the 
lowest grades to short periods. 

35. Ai>plieation of Drills to Practical Examples. 

It will be found of the highest value to carry along with the 
foregoing drills a corresponding work on slate and black- 
board. It would be absurd, of course, to ask pupils to solve 
examples involving division by 9 before they have mastered 
the drill as far as 9. But just as soon as they have learned 
a new step, they should be taught what it is to be used for, 
and they should be made thoroughly familiar with the 
method of using it. We make a serious blunder when we 
attempt to master all the tables before we try to apply them 
in practice. No one any longer attempts to have children 
inaster the entire alphabet before he introduces them to easy 
words and sentences. Many children are now taught to read 
quite well before they are sure about the identity of certain 
rarely iised letters such asy, .c, and q. 

This failure to apply to some definite practical use each 
merely mechanical, abstract matter as soon as it is learned, 
is what robs the earliest school work of the interest it might 
otherwise have. All our best authorities on pedagogics are 



§ 1 PEDAGOGICvS OF ARITHMETIC. 37 

urging- the importance of coordination and correlation in the 
matters that are taught. 

36. Frequent Reviews a Necessity. — One of the dis- 
coveries that every teacher of young children is sure to make 
is the discouraging fact that no matter how carefully a sub- 
ject is taught it is certain to be forgotten in a very short 
time. When oin^ pupils come back to us after the summer 
vacation we are astonished to find that they have nothing 
better than a vague and confused remembrance of the impor- 
tant things we taught them with so much painstaking. Phys- 
iologists tell ns that this is owing to the fact that the brain of 
a child is growing and changing with great rapidity. After 
the cranium has reached its full size, impressions that are 
deeply made are likely to be permanent; but before that 
time they are, so to speak, overgrown and hidden b}^ 
encroaching brain tissue. Moreover, by the time that we 
have nearly or quite attained maturity, the mind is stored 
with much information of every kind, and with this any new 
idea is easily and closely associated. It is then easy to 
remember the new fact by the aid of association and likeness. 
Of the occurrences that make up our life before the age of 
six years, nothing, or almost nothing, is remembered when 
we reach mattn-ity. It is only by repeating again and 
again those early lessons that we may expect to have them 
endure. Let every matter that you teach in those first years 
of the child's school life be carefully predetermined, and 
reviewed until it cannot be forgotten. Remember that this 
is a period of accumulation and for the establishment of 
tendencies rather than a period of definite development. 
There should be no "lost motion" in education — no wasted 
effort. Therefore, work systematically, and do not be dis- 
couraged at apparent forgetfulness on the part of your 
pupils. Above all, review and review again. Your work is 
much like making- an artificial island where shallow waters 
rest upon unknown depths of sediment. If the material for 
filling is not too widely scattered, a support for the super- 
structiu-e will ri.se above the surface sooner or later. 



38 PEDAGOGICS OF ARITHMETIC. § i 



NOTATio?^ A:N^r) nijmeratio:n. 



ARABIC NOTATIOX. 

37. The Perception of Number. — A very ciirious and 
interesting question of psychology is this: 

How many objects of the same kind, without arrangement 
in groups, is the mind capable of instantly perceiving ? 

If three separate bright points were to appear for an 
instant on a dark background, and vanish at once, even if 
there were thousands of observers, all would probably agree 
as to the number of illuminated points. If a bursting rocket 
on a dark night should show four such bright points, the 
difficulty would be only very slightly increased. If the 
number were increased to five^ or even to six^ any one 
catching the fleetest view of them would be very likely to be 
certain of their exact number. Much experiment has shown 
that about seven is the limit to the instantaneous perception 
of number, unless objects are in groups each containing a 
known number of units. 

Beyond the number seven, the mind's inability to take in 
at one act the several units that make up a collection, begins ; 
and its helplessness becomes rapidly more apparent as the 
number increases. This fact has an important bearing on 
the question of teaching notation and numeration — the wri- 
ting and reading of numbers. 

When a person of normal mind hears the expression, 
"three apples, "he immediately forms a mental picture or 
image in which the objects named appear represented in a 
group, very much as in an ordinary picture. If, however, 
the expression be "twenty-nine apples," no such picture is 
formed. No attempt is made to conceive them as separate 
imits, for the task is beyond the power of the mind, which 
is very quick to perceive its impotency. But what does 
happen in the mind ? Very nearly the same that happens 
when such expressions as " many apples," "much money," 
and the like are heard. Nothing very definite perhaps; but 



§ 1 PEDAGOGlCvS OF ARITHMETIC. 39 

it is certain that the mind sees nothing to correspond to the 
three or four bright points mentioned above. If, however, 
we insist upon forming a mental picture to represent such 
expressions, the mind will in every case .seek the easiest 
way of doing it. In the case of large numbers, this easiest 
way is to form a mental picture of the Arabic figures that 
express the numbers. Thus, the simplest form in which the 
mind can carry the number three hundred sixty-seven is 
the mental image of 3G7. If the ear hears the spoken num- 
ber at the same time that the eye sees its written or printed 
form, the greatest possible distinctness of mental effect is pro- 
duced. The action of the brain center that takes cognizance 
of sound strengthens and reenforces that of the brain center 
that responds to visual impressions. Every teacher is aware 
of the double effect produced upon the mind by addressing 
both the eye and the ear in teaching- any subject. 

It is clear, then, that the mind makes no attempt to con- 
ceive of large numbers by separating them into their com- 
ponent units; that, on the contrary, it seeks the way of least 
diiffculty — the " line of least resistance." 

38. Ajiplicatiou to Pedag'og'ics of tlie Forego in j? 

Fact. — About twenty years ago one of the leading educators 
in this country published a very remarkable arithmetic. 
Believing that children should be habituated to the mental 
operation of exactly conceiving the real significance of the 
numbers they handled in their arithmetical work, he devoted 
many pages to an elaborate treatment of notation and nmner- 
ation. Very excellent and abundant were the illustrations 
employed. Beginning, he showed by means of pictured 
straws the numbers up to ten. Then, by a bundle of ten 
straws, placed in turn before two, three, etc. separate straws, 
he represented the numbers between 10 and 20. Two ten- 
bundles and nine straws represented 29; eight ten-bundles 
and five straws formed the visible representation of 85. Ten 
ten-bundles made the next measuring unit — the 100-bundlc, 
and the pupil was expected to see in the number 958, 
for example, nine lOO-bundles, five ten-bundles and eight 



40 PEDAGOGICS OF ARITHMETIC. § 1 

separate straws. Finally, ten lOU-bundles were made into 
a 1,000-bundle, and great ranks of these were formed to 
represent such numbers as 7,89o. But the author stopped 
at this point, and the fact that he did suggests the question 
why he did not stop earlier. 

Where is the proper place to give up the task of helping 
the mind to distinct conception of the real meaning of num- 
bers ? Opinions differ. One thing is certain; no one in 
actual life analyzes numbers to this extent, nor does any one 
ever need to do so. If seven or eight is our mental limit, 
why should we undertake a task that is both hopeless and 
needless ? Sooner or later we come to deal with numbers so 
great that we could not adequately conceive them even if it 
were necessary. Why not, then, give up the useless work as 
soon as possible ? 

In higher mathematics, quantity is represented by letters 
and other symbols of general value, and one of the great 
advantages of this is that the mind is not diverted from 
necessary operations with these symbols by any attempt to 
gain an exact conception of the aggregates denoted by the 
general symbols. It is pretty evident that if the work of 
analyzing numbers be kept up very long there will be estab- 
lished a tendency to analyze every number entering a 
problem, and, thus, the power of the mind to reason about 
the conditions of the problem itself will be correspondingly 
diminished. The application to pedagogics of the foregoing 
considerations seems to be the following: 

Teach the Arabic sy stein of notation and numeration — the 
decimal system — so that the pupils shall thoroughly compre- 
hend its essential principles, but do not carry much beyond 100 
the minute analysis of number. 

The fact is that life and the world are full of number, 
and even if we try to escape knowledge of number, — more or 
less definite, — all indeed that we really require for the uses of 
life, we cannot do so. Besides, there is no more real necessity 
that we should conceive definitely of the real meaning of the 
great numbers emplo3'ed in arithmetic than there is that we 
should know exactly how many units are intended by the 



§ 1 PEDAGOGICvS OF ARITHMETIC. 41 

expressions, "a crowd of people," "a flock of birds," 
"myriads of stars," "a long- time." We are able to think 
and to talk about these collections very satisfactorily, with- 
out knowing- the number of units that make up their aggre- 
gates. We have been so long and so often baffled by our 
conditions and limitations that the mind has forgotten its 
instinct to demand a sharp and clear mental picture for 
every object that engages the attention. 

39. Importance of the Lang-iiag'e of Xunibei'. — In 

dealing with numbers in computing, we must know how to 
write and to read them. This is a form of number knowl- 
edge that is of very great importance, for without it the 
teaching of arithmetic would be a task of extreme difficulty. 
Our children must be taught to write and read numbers 
expressing vague magnitudes so great that even the greatest 
mathematician would be unable, adequately, to conceive 
them. It is the language of number that is important; its 
real meaning beyond the first three or four figures has very 
little practical value or interest, and should be neglected in 
teaching. No one is ever conscious of an imperative mental 
demand to know the exact significance of a number composed 
of many figures, and yet we use them in computation wdth 
the same facility that we do numbers of small value. The 
newspapers often contain curious attempts at conveying, by 
means of ingenious comparisons, approximate notions of great 
numbers, such as national debts, atomic or molecular particles, 
stellar distances, and the like; but these are only curiosities 
of measure ; they have no educational value whatever. 

The writer believes, then, that pupils should know very 
intimately and familiarly all whole numbers up to 100, and 
somewhat less exactly the nmnbers as far as 1,000 or at the 
farthest 10,000; in addition to this he should understand the 
theory of the Arabic notation and numeration well enough 
to write and read numbers as far as they have any real 
human use or application. Perhaps, not more than one per- 
son in 100,000 could readily write and read numbers as far 
as vigintillions, and one might pretty safely assert that no 



42 PEDAGOGICS OF ARITHMETIC. § 1 

person has ever been confronted with a real necessity for 
doing so. It should be on the real utilities of the school 
curriculum that teachers should employ their strenglh. 

40. Two Methods of Teacliing [Notation. — The 

names of numbei'S may be taught by two very different 
methods, distinguished as the couiiiwn uietJiod and the scien- 
tific method. As far as to ten these methods are alike, the 
work in each being to make pupils perfectly familiar with all 
elementary combinations up to that limit. The common 
method proceeds with numbers beyond ten just as with 
numbers expressed by one figure. Twelve, sixteen, and 
twenty are taught in exactly the same way that six or nine is. 
No attempt is made to have pupils see toi or tlwcc in the 
word thirtccji, or to learn the principles of the decimal scale. 

In teaching by the scientific method, when ten is reached, 
the idea of a ten-group is taught, and then the numbers 
between ten and twenty are each only this ten-group with 
an addition. Thus, thirteen is t/ircc-tcn, fifteen is fivc-tcn, 
etc., the names being exactly similar to the Latin trcdcciin^ 
guindcciui, etc., and to the Greek -peLOKaideKa, tj'ciskaidcka, 
' ' three-and-ten, " TrevreKatdsKa, poitckaidcka^ ' ' five-and-ten, " 
etc. In our words eleven and twelve the cue to the decimal 
scale is not so obvious as in the Latin 7/;/<r/rr/w, "one-ten," 
^.nd duodecini, "two-ten, "or in the Greek "vdeKa, /leudeka, 
" one-ten, " and 6(l)d£Ka, dodeka, " two-ten. " 

When twenty is reached, the English word still shows the 
decimal scale, for it is derived from the Anglo-Saxon tzvegen, 
"two," and tig or ty, "ten." Twenty is, therefore, much as if 
it were written tivain\.y^ for tzvain is the modernized form of 
tiuegcn. Thus, by the scientific method, the teacher con- 
tinues his work by showing that thirty means three-tens ; 
forty, fonr-tcns ; and so on to one hundred. At this point 
he shows that a hundred-group is made of ten ten-groups, 
after which the pupils can proceed with the work of writing 
and reading numbers to one thousand. Here again, ten 
hundred-groups make a new group called the thousand- 
group; and so the work goes on. 



§ 1 PEDAGOGICS OF ARITHMETIC. 43 

In both the common method and the scientific method, it 
is necessary to teach that numbers are divided into gToiips 
of figures called periods; that these when full contain three 
fig-ures each; and tltat, beginning at the right, they are 
named in order, units, t/ioiisaiids, millions, billions, etc. 

There is no doubt, whatever, that the scientific method 
is by far the better; for, taught in this way, children, 
in a very brief time, will both write and read numbers with 
facility. 

41. Tlie Teaching: of " Oinlers." — Many teachers con- 
sume much time in teaching what is known as the "orders" 
in the decimal system. These orders or places are some- 
times called by names, as the order of units, the order of 
tens, the order of hundreds, etc. ; again they are designated 
as Jinits of the 1st order, units of the 2d order, etc. To do 
this is worse than time wasted; it serves to complicate with 
unnecessary verbiage a subject that is very simple. There 
is not the slightest use for all this in teaching notation and 
numeration either by the common method or by the scientific 
method. We frequently hear teachers ask their pupils to 
numerate a number before reading it. By this they mean 
that the orders shall be named in succession from right to 
left. Thus, suppose that the number to be read were 

307,425,010,001. 

The pupil is expected to point, and to say as he points, 
"units, tens, hundreds, thousands, ten-thousands, hundred- 
thousands, etc." This is supposed to help him in reading 
the number, but in reality, it serves only to determine the 
name of the left-hand period. But this may be done much 
better and more quickly by naming the periods — not the 
orders. Thus, for reading the number above, all the numer- 
ation required is to say " units, thousands, millions, billions." 
We are then able to read the number by beginning with 
billions and giving the period names in descending order. 
The pupils should, of course, know period names and their 
order, in both directions, very thoroughly. 



44 PEDAGOGICS OF ARITHMETIC. § 1 

43. Use of "•And"*' in Reading Numbers. — During 
recent years many textbooks on arithmetic and many of the 
most careful teachers have been insisting that the word and 
should be used only as a substitute for the decimal point in 
reading numbers. Thus, 365,407 should be read ''three 
hundred sixty-five thousand four hundred seven," not 
"three hundred and sixty-five thousand four himdred and 
seven. " The advantage of this will appear when we endeavor 
to distinguish between two such numbers as the following 
by the manner of reading them : 

505,000 — read, "five hundred five thousand." 
500.005 — read, "five hundred and 'avQ thousandths." 

In ordinary conversation the word and is used between 
dollars and cents, but bookkeepers and others that must 
constantly mention sums of money, regularly omit and. 
Thus, I may say, "His bill is twenty-five dollars and 
seventy-five cents"; but in actual business this is rarely 
done. In school, whenever sums of money occur in reading 
or dictating examples, something is gained both in time and 
precision if the conjunction is omitted. The case is the same 
in reading and writing ordinary denominate ntmibers. 

$18.758 — read, "eighteen dollars seventy-five cents eight mills." 
3 yd. 2 ft. 9 in. — read, " three yards two feet nine inches." 

43. The Decimal Base. — It was noticed in Art. 40 
that the words eleven and tice/ve contain no etymological 
hint of the decimal system. It is only when thirteen is 
reached that the method of grouping by tens is wrapped up 
in the word itself. The decimal system is supposed to have 
had. its origin in the method of counting the fingers, but 
many mathematical writers are agreed that we are by no 
means fortunate in the base of our numerical system. 
Leibnitz thought that 2 as a base would have been more 
convenient, and he actually wrote an arithmetic with the 
binary scale. Charles XII, of Sweden, a short time before 
his death at the battle of Llitzen, expressed his intention of 
introducing the duodecimal system into his country. 



§ 1 PEDAGOGICS OF ARITHMETIC. 45 

We hear much of the excellence of the decimal system, 
but there is no doubt that the duodecimal system would have 
been much better. This becomes apparent from several 
facts : 

1. The decimal system is arbitrary and iiiuiatural. If the 
inventors of the Arabic notation had endeavored to get a 
suggestion from nature's method of grouping, they would 
never have chosen ten as the base; for nature groups by 
twos^ by t/irees, hy fours, fives, and sixes, but very rarely by 
tens. Man instinctively doubles, triples, and quadruples; or 
he divides into halves, thirds, and fourths. These are, 
therefore, nature's multiples and submultiples, and a scien- 
tific base should be one that would exactly contain 2, 3, 
and 4, and that, hence, could be exactly subdivided into 
halves, thirds, and fourths. With 10 as a base this is not 
possible. 

2. The decimal system is nnscientifie and inconvenient. 
This is evident from what is stated above. For the human race 
to group and subdivide naturally in one way, and arithmet- 
ically in another, is like trying to use a tool unsuited to the 
shape of the hand. We are so familiar, however, with the 
decimal system that we are unable to compare it with any 
other, for we know no other, but a brief study of the general 
subject of the scales of notation in higher algebra very soon 
reveals the fact that there are better systems than the one 
we have. 

44. Advaiitaares of the Duodecimal Scale. — The 

duodecimal scale would be better by far than that of which 
the base is 10. Were 12 the base, we could express in one 
decimal place \, \, \, i, and J^; or, in order, .6, .4, .3, .2, 
.1; \ and \ would be .18 and .10. With the decimal scale, 
\ and i require one decimal place, .5 and .2; ^ requires two 
places, .25; and \ is expressed by three deciinal places, .125; 
but \, \, i, and -g- cannot be written in a finite decimal that 
terminates. 

The advocates of the duodecimal .system call attention to a 
tendency to reckon by the duodecimal scale, indicated by the 



46 PEDAGOGICS OF ARITHMETIC. § 1 

many things that are bought and sold by the dozen, the gross, 
and the great gross, to the division of the year, the circle, 
the foot, the Troy pound, and to the fact that we carry the 
ordinary multiplication table to 12, and carry the one-figure 
method of multiplication and division as far as to 12. It is 
asserted, also, that many languages show signs of a natural 
tendency to 12 as a scale, as we see realized in our own names 
eleven and twelve. It is, however, certain that no change 
will ever be made, even though it were made veiy clear 
that such a change would be highly advantageous. 



ROMAX XOTATIOX. 

45. Inferiority of Roman Notation. — Faulty though 
it may be, the Arabic notation is the only method of express- 
ing numbers ever devised that is worthy of the name. By 
no other system in use is it possible to perform rapidly and 
accurately the fundamental operations, or to compute powers 
and roots. In the days of ancient Greece and Rome, what 
we now know as banking, with bookkeeping an exact science, 
was practically impossible. Cashiers and paying tellers 
could have "gone wrong" with impunity, for no "expert" 
in bookkeeping could have gone over the books and have 
shown the exact amount of the peculation. 

How much are Europe and the United vStates — the whole 
world, indeed — indebted for progress and civilization to the 
introduction of our present system from an Arabic book in 
the 12th century? No one can tell with any certainty; but 
we may be very sure that the resources of the Roman 
notation — the best of all except the Arabic — would not have 
availed for the inathematics of science, art, and the various 
industries of today. No period of great achievement in 
science, engineering, and industry would be possible if there 
were no better systems of notation than those employed 
among the Greeks and the Romans. 

Roman notation is still retained in many of our textbooks 
on arithmetic, and is taught in many of our schools, but there 



§ 1 PEDAGOGICS OB^ ARITHMETIC. 47 

is, perhaps, no real reason why this should be done. The 
system is used to some extent in numbering chapters, in 
paging, and in many other ways. In medical prescriptions, 
it is used, but with some slight modifications. In these 
prescriptions final / is always written as/, and to denote one- 
half, ss {scjuis) "half" is used. Thus, if your physician 
wishes to indicate 18^ drops of paregoric, he does not say it 
in plain English, but he confronts you with Opii cavipJiorati 
ti)ict., in. xviijss. One feels less reluctant to pay a good 
round price for a medicine with a name so learned as that. 

4G. ?^ecessai'.v Instruction in Roman dotation. 

It is not quite certain that there is any real need of formally 
teaching, in school, this system of expressing numbers, for 
it is one of the matters very quickly " picked up," if circum- 
stances require its use. Most teachers have children give 
the numbers of reading lessons, and this soon makes them 
familiar with the notation as far as one hundred. Very 
rarely is any use made of it beyond this point. 

However, if circumstances or the course of study should 
require it to be taught, to do so is a very simple matter. The 
following statement covers the entire subject : 

Seven letters are employed in Roman notation. They are 
I, V, X, L, C, D, and M. These, taken separately, stand, 
respectively, for the following numbers: 1, 5, 10, 50, 100, 
500, 1,000. Combined in accordance with the following 
principles, every number may be expressed : 

1. A letter standing alone represents value as explained 
above; with a horizontal line above a letter or a eonibination 
of letters, the value is nniltiplied by 1,000. 

X = 10, L = 50, V = 5,000, M = 1,000,000. 

2. Repeating a letter repeats its value. 

XX = 20, CCC = 300, MM or 11 = 2,000. 

On the dials of clocks and watches IV is expressed by II II ; 
either CCCC or CD denotes 400; otherwise no letter is 
ever used more than three times in one combination. The 



48 PEDAGOGICvS OF ARITHMETIC. § 1 

letters V, L, and D are never repeated in expressing any 
number. 

3. Whoi a letter fo/lo-ws one of gi'eater value, their sitin 
is denoted ; tvJien the order is reversed, their difference is 
denoted. 

XI = 11, LXVI = G6, CLXXVI = 170; but, 
IX = 9, XLIV = 44, XCIX = 99, CDLXIX = 4G9. 



THE TEACIIIlSrG OF FRACTIONS. 



MATTER AND METHOD. 

47. Preliminary. — Some remarks on the subject of 
fraction work have already been made in this Paper (see 
Art. 8). The student will do well to read that article again 
very carefully before resuming the subject at this point. 
The writer is convinced by an experience of rnany years 
that all the fundamental operations, as well as all the various 
forms of reduction of simple fractions, may be mastered by 
young children with perfect ease and constant delight ; that 
fractions are in no respect more difficult than integers, 
and that they should be studied at the same time with 
integers. He believes that children are quick to take for 
granted that fractions are only integers made by subdividing 
larger integers, just as a board is a unit arising from the 
subdivision of a log, or a pint is a unit derived from a quart 
or a gallon. Indeed, most people would be surpri-sed to be 
told that a foot, or a slice of bread, or a dime, or a scuttle 
of coal is just as mucli a fraction as it is an integer. The 
subject has been invested wnth difficulty by the manner in 
which it has been treated, and many educators are coming 
to see the seriousness of the blunder we have been making 
so long. And the students we teach so badly, many of 
them become, in their turn, teachers, and help to perpetuate 
the error. 



§ 1 PEDAGOGICvS OF ARITHMETIC. -4!) 

48. Some Conditions of Success iu Teacliing Frac- 
tions. — In this, as in every other subject, the success with 
Avhich a teacher handles it will depend principally on the 
thoroughness of his mastery of it. He must see it, not 
vaguely and partially, but in its very essence, clearly and 
completely. Unless he is familiar with it as a whole, in its 
parts and their relations, and in its various methods, proc- 
esses, and principles, he cannot teach it with that intelligence 
and enthusiasm that will make it a source of delight to his 
pupils. 

But, suppose that the teacher lacks this admirable prepa- 
ration — what then shall he do ? Shall he do as his teacher 
probably did with him — delay all notice of fractions until 
the pupils have studied ordinary integers for three or four 
3'ears, and then teach them the fractional routine, — the mere 
mechanical processes, — omitting all attempts to have the 
real meaning of fractions, and the reasons of the operations 
with them, understood? This, by no means; rather should 
the teacher remember that, even late, it is possible to learn 
to do well that which we have been doing indifferently or 
badly. If we are willing to give careful consideration to the 
subject, to formulate a new plan based upon the best infor- 
mation we can get, and then execute it steadily and without 
wavering, success will come at last. But it is certain that 
whatever theory or method we adopt, we shall find many 
difficvilties in working it out in practice. If we are really 
capable, earnest, and resourceful, we shall never reach our 
object in exactly the same way as we did the preceding term 
or year. vSome modification will be suggested by changed 
circumstances, some on account of faults we noted in our 
previous method. All these are signs of growth in our- 
selves; we are becoming wiser in the safest and surest 
manner — experience. 

49. The Plan in General. — The student has, doubtless, 
by this time obtained a pretty accurate notion of the method 
of teaching fractions that is recommended in this Paper. It 
is important, however, that no chance should remain of being 



50 PEDAGOGICS OF ARITHMETIC. § 1 

misunderstood ; so that it is necessary to indicate again the 
general plan, as follows: 

1. TJicrc is no essential difference between integers and 
fractions. 

All the fundamental operations that can be performed with 
integers can be performed in exactly the same way with 
fractions. Thus, we may add 3 fifths and 3 fifties just as 
we add 2 apples and '.} apples ; we may subtract 3 fonrths 
from b fonrtlis, or multiply 3 thirds by 5, or divide 8 thirds 
by 2 or by any other divisor. It is true that ^ cannot be 
added to \ or to \, just as you cannot add oranges to apples 
and obtain a sum with a single vieasnring unit. But a very 
simple operation will reduce unlike fractions to forms that 
can be added or subtracted. This is very similar to the 
reduction required in such examples as the following: 

(c?) When apples are worth 3 for 1 cent and peaches 
2 for 1 cent, what is the value of 12 apples and 12 peaches ? 

(/'') If 3 apples are exchanged for 2 oranges, and 5 peaches 
for 3 oranges, how many oranges should be given for 12 apples 
and 20 peaches ? 

2. /// the first easy oral work with nninbers., ordinary 
units and fractional units should not be separated. 

Of course, it is assumed that the teacher will understand 
how to graduate this work with respect to difficulty. If 
exercises, either in integers or in fractions, are of too great 
severity, the pupils are simply discouraged and nothing is 
accomplished. The plan here proposed contemplates noth- 
ing more than to have the pupils become acquainted with 
the simplest fractional division of all kinds of concrete units, 
after which they may pass to the abstract forms, \, \., |, \, etc. 
This they will do very easily and with much pleasure. When 
they know exactly what thirds are, they wdll readily add, 
subtract, multiply, and divide them, and employ them in 
appropriate easy analyses without noticing that they are in 
any respect different from integers. Such terms as numera- 
tor, denominator, terms, lowest terms, common denominator, 
and others strictly technical need not be mentioned during 
this period. 



§ 1 PEDAGOGICS OF ARITHMETIC. 51 

3. Only the simplest fractions should be used, and no con- 
crete unit should be divided into unusual parts. 

When a child is perfectly acquainted with the coml)inations 
of integers tip to and including- 4^ he is able to handle halves 
and fourths. Having reached 0, he can deal with halves, 
thirds, and sixths. He can change halves to sixths, thirds 
to sixths, and the reverse ; within his narrow limits he can 
perform with them any operation that he can perform with 
integers. 

The necessity of avoiding, in all stages of the work in 
arithmetic, every unusual division of concrete units is some- 
thing that even to suggest might seem superfluous, but it is 
only a few years since the arithmetics contained problems 
and answers to problems in which you might find such 
fractions as 4- of a man or other living animal, fV of a yard, 
i| of a day, f of a cpiart, etc. Now, we know that gallon's, 
yards, miles, feet, bushels, tons, etc. are all divided very 
definitely in actual practice. It would be a difficult task 
to measure exactly any such matter as ^ of a gallon or -^-j of 
a yard. 

The teacher should be particular, in this early work, to 
use only the simplest units for .subdivision and to employ 
only easy fractions and such as are actually used. By observ- 
ing this rule, the children may incidentally get much useful 
knowledge about the measures in common use, such as the 
pint, quart, and gallon ; the yard, foot, and inch ; the pound 
and ounce, etc. 

50. First Lessons AYitli Halves, Thirds, and Fonrths. 

It has been stated that the study of halves may begin with 
the study of 3. Similarly, thirds, fourths, fifths, and sixths 
may be introduced at the same time w^th 3, 4, 5, and G. But 
there is little that can be done with halves, beyond learning 
what they are, imtil the child has gained a mastery over num- 
bers greater than 2; and the same is true of thirds, fourths, 
and fractions of less value. It is clear, then, that the very 
first lessons with fractions should aim at nothing more than 
making the children perfectly aware of what is meant by these 



53 PEDAGOGICS OF ARITHMETIC. § 1 

various subdivisions of the unit. The lessons should at first 
deal with objects that are capable of easy division into equal 
parts. One of our educational writers advises that at first 
the teachers should use objects that "lose their unity by 
subdivision, " such as apples, potatoes, etc. ' ' A splint broken 
or cut in two becomes tivo splints, not halves of one splint," 
he says. But it may be added that the objects used should 
be capable of separation into parts that appear to be exactly 
equal; otherwise, the pupils will fail to get the idea, which 
is very important, that ' ' halves of the same thing or of equal 
things are equal." 

The blackboard furnishes the best possible means of illus- 
tration. The teacher may draw a circle on the board and have 
the children imagine it a pie or an orange to be equally 
divided among several ; a heavy straight line may be called 
a ribbon, a stick of candy, or other object of length. The 
pupils may be called upon to divide with crayon lines that 
represent familiar objects. And these representations of 
objects are just as effective in helping children towards a 
definite conception of pure abstract number as the reality 
itself, for their most active faculties at this time are the 
reproductive — the powers, of memory, imagination, and 
fancy. 

The first lessons in fractions, then, should attempt no 
more than the work indicated below, but this should be 
thoroughly done, and every step should be abundantly 
illustrated by objects. When it is certain that the pupils 
are perfectly familiar with the idea of 2, the following 
should be taught very carefully, and afterwards frequently 
reviewed. 

1. The meaning of Jialf and lialvcs. Teach pupils to 
recognize and pronounce these words when written, not 
printed, on the blackboard. As soon as they are sufficiently 
advanced, they should be taught to write them correctly. 

2. The meaning of the forms \ and \. The pupils should 
know also that ^ and onc-ltalf xw&^xi the same thing. 

o. The use of signs in the following: 1 =: |; |- = 1; 
i^.^ = I; i_^ — I; 2_^ _ I These equations should 



§ 1 PEDAGOGICS OF ARITHMETIC. 53 

be developed from illustrations on the blackboard. Require 
the pupils to write these equations on their slates, and see 
that they know exactly what each means. 

4. Begin the "arithmetical storytelling." For example, 
let the teacher write on the board the equation, 

1 + ^ = 1, or f-| = i 

and, then, to show them what he wants done, let him illus- 
trate by two or three "stories." These should contain no 
word with which the children are not perfectly familiar, and 
the sentences should be short. As each symbol in the equa- 
tion is brought into the story, the pointer should indicate it. 
The story in every case should be the equivalent of an 
example and its solution. The following' will show what is 
meant : 

" Once there was a girl whose name was Mary. Mary had 
a little sister Katy and a little brother Arthur. She gave 
half of an orange to Katy and half of an orange to Arthur. 
So, she gave them one-half of an orange a)id (later, phis) 
one-half of an orange; that would be one whole orange." 
Success here will depend much on simplicity of language 
and vivid earnestness of manner. It would not be easy to 
find a better exercise in language training. 

51. Sclienie of I^ater Fraction Work. — The work 
described in the foregoing article may be continued on 
halves, thirds, and fourths for several weeks. In the 
meantime, the study of integers is progressing in an orderly 
way imtil the pupils have become quite expert as far as 10 
or even 12. When they have reached 12, there is no elemen- 
tary exercise in fractions that needs to be withheld from 
them. The following scheme of graduated oral exercises 
will be found helpful. The teacher should remember, how- 
ever, that if real difficulties are introduced too early, this 
and every other scheme will fail. Do not discourage your 
pupils for the sake of puzzling them. The ability to assimi- 
late the food we take is no more important to the growth 
and health of our physical powers and organs than it is 



54 PEDAGOGICS OF ARITHMETIC. § 1 

to be able to assimilate the matter taken for mental 
development. 

In the following plan the work is mostly with halves and 
thirds, but it is clear that when the children are well 
acquainted with integers as far as 12, they are ready for 
exercises with halves and fourths; thirds and fourths; halves, 
fourths, and eighths; thirds and ninths; halves, fifths, and 
tenths; halves, thirds, fourths, sixths, and twelfths. vSuch 
fractions as have prime numbers for their denominators, as 
sevenths, elevenths, etc., are rarely used in actual practice, 
and should be deferred until the time for the general treat- 
ment of fractions, at the close of the primary, and the begin- 
ning of the grammar-school period. 

53. Order of Topics. — The following is the scheme in 
detail of oral work in fractions: 

1 . Change integers to halves and to thirds ; also the rever.se 
when the change involves no mixed numbers. Do not 
neglect abundant illustrations. 

2. Change mixed numbers to halves; as, 1^, 2^, etc. ; also 
mixed numbers to thirds; as, 2^, 1|, etc. Reverse these 
two operations. Require pupils, finally, to announce results 
instantly. 

3. Given, the cost, length, etc. of ^ of anything, to find 
that of the whole. 

4. Given, the cost, length, etc. of i of anything, to find 
that of I of it, and of all of it. 

5. Given, the cost, length, etc. of the whole of anything, 
to find that of i i, and f of it. 

G. Knowing the cost, length, etc. of a yard, pound, etc., 
to find that of a mixed number of the same. Use very sim- 
ple numbers that will give integral results. 

7. Knowing the cost of 1^, 2^, 1^, If, etc. yards, pounds, 
etc. of anything, to find that of the unit. Use diagrams 
freely, planning them beforehand. Copy and save such as 
yoii find to be good. 

8. Exercises in adding halves; as, ^-hf, i + f + l-, etc. 

9. Exercises in adding mixed numbers containing halves ; 



§ 1 PEDAGOGICvS OF ARITHMETIC. 55 

as, 1^+2^, 4 + l^ + 'H. Add integers and fractions sepa- 
rately, and unite results. This work should also be written, 
in vertical columns on the board, copied on slates by the 
children (very neatly), and done without the help of the 
teacher. 

10. Exercises in adding thirds; as, -g-+f, f + i|+|, etc. 

11. Exercises in adding mixed numbers containing 
thirds; as, If + ^^i' 'H + -i|- + lf- Slate work with vertical 
columns. 

12. Subtracting mixed numbers containing halves. There 
are three cases: (a) when the difference is an integer, as, 
71 — 3^; {I?) when the subtrahend is an integer, as, 7|- — 3; 
(c) when the minuend is an integer, as, 7 — 3^. This last 
case should be solved in two steps: 7 — 3 = 4; and, 

4-i = ^. 

13. Exercises in subtracting mixed numbers with thirds. 
The following examples illustrate the varieties: 5f — 3, 
5i-3^, 5f-3i 5-31 5i-3f. The last example should 
be solved in three operations. Thus, 5 — f = 4|-; 4:^ — 3 — 1\; 
11 + i = If. That is, 

(a) Take the lower fraction from the upper viteger. 

{I)) From the remainder take the lower integer. 

(r) Add 70 hat still remains to the upper fraction. 

The explanation of the reasons may be deferred. The 

advantages of this method over that in common use are : that 

in slate work nothing need be written but the answer; that no 

thread of the argument is let go while a necessary reduction is 

made; that, therefore, the operation is not interrupted at any 

point; that the method is general. To illustrate these 

important points, let it be required to subtract 4f from Of. 

The ordinary solution, when written, is shown 
9^ = QJ*- = 8-" • 
43 _ 4? _ 4y 11"^ the margin. The break in the operation 

~ ~^ -~ comes when the pupil tries to avoid writing 
^"^ all these reductions. He first notices that 
he must reduce the fractions to twelfths. He then dis- 
covers that y»2 cannot be taken from ^^. This is a decided 
check. He lays aside his yV, the reduced form of f, while 
he borrows a unit from the minuend, changes it to twelfths, 



56 PEDAGOGICS OF ARITHMETIC. § 1 

and proceeds to add it to f . By this time he has probably 
forgotten that f = j\, and may, therefore, have to do again 
the work of reducing | to twelfths. But, finally, he gets the 
value of 1 + f ii^ twelfths, and is ready to take from f^ the f . 
He discovers now that he has forgotten how many twelfths 
there are in | and he lays aside his ff while he may reduce 
f to twelfths; and when this work is done, his ff is probably 
forgotten. The method is one of much ' ' backing and 
filling." 

By the other method, nothing is laid aside to be probably 
forgotten while some other part is being prepared for use in 
the operation. The steps are finished one by one, and are 
never resumed. For the example in question, these steps are : 

Example. — 9| — 4|. 

Operation.— 9-f = 8J; 8:^-4 = 4|-; 41 + 5 = i-i^ + ii = 4^-- 

14. Exercises combining addition and subtraction of 
mixed numbers with halves, as, 4^ + 3 — 2^, 5^ — 3^ + '^h ^^c. 

15. Exercises, as in (14), combining thirds; as, 
4f — 1^ + 3f . In connection with work of the kind indicated 
here and in (14), many concrete practical examples should 
be made and solved. The teacher should first make a few, to 
give an idea of how it should be done, and afterwards require 
the pupils to make them. After the pupils have reached the 
proper stage of progress, it is well to have them write these 
examples on their slates. 

16. Add halves and thirds in combination; as, ^ + 1^ 
f+li 2i + 3f+H, 3i + 4i+U + 2i + i- In such cases 
as the last, add the halves first, then the thirds, combine the 
results, add the integers, and, finally, combine with the sum 
of the fractions. Practical examples. 

17. Subtract halves and thirds; as, -j — ^, f — i, 2f— 1^, 
5^ — 2|, etc. Make the pupils very familiar with the follow- 
ing equations: i = f , i = f , f = |. 

18. Mixed addition and subtraction of halves and thirds; 
as, 3^ — If + 2i> etc. This is suitable for slate work. Orally, 
such work should be done in three steps: 

(,,) 3-1 + 2 = 4; (^) 4 + i + l- = 4|; (c) 4|-f = ^. 



§ 1 PEDAGOGICS OF ARITHMETIC. ST 

That is, 

(a) Find the total of the ijitcgcrs in accordaiico ivit/i the 
signs. 

{(3) To tJiis total add the fractions that are affected by the 
pins sign. 

(y) Diminish the second result by the negative fractions. 

19. Multiply \ and \ by various integers, changing result 
to whole or mixed numbers; as, ^X 5 = f = 2|-; |-x8 = f 
= 2|. Many practical examples. Illustrate. 

20. Multiply |, f, f, etc. by integers, reducing result. 
Same exercise with f, f, 4, etc. 

21. Multiply mixed numbers with halves and thirds by 
various integers; as, 1^x4, lfX2, 2^X5, etc. Concrete 
examples. vSolutions should be in the fewest possible words. 

Example. — Let it be required to multiply 3^ by 4; also, 3| by B. 
Solution. — 4 times 2\ is 8 and -|, or 9i; 3 times 3f is U and |, or 11. 

Do not permit the pupils to say, "4 times \ is I, or 1^; 
4 times 2 is 8; 8 + 1^ is 9i." 

22. Exercises to make the pupils familiar with the fact 
that such forms as 4-X 5, \ of 5, and 5 X ?r are equivalent. 

23. Find ^, 4, and \ of integers ; first, when the result 
is exact; second, when the result is a mixed number. Con- 
crete problems. 

24. Show by diagram that \ of \, or i of \, is i. This may 
be done by figures of many kinds; as, for example, by divi- 
ding circles, rectangles, or simple straight lines, as below. 

{a) To show that ^ of i = i (Fig. 9.) 



I I 2 ' 2 2 

6 6 6 6' 6 

Fig. 9. 



(b) To .show that i of ^ = f (Fig. 10.) 



iofi 



Fig. 10. 



58 PEDAGOGICvS OF ARITHMETIC. § 1 

25. Find ^ of i |, |, f, etc. Then i- of 1|, 2^ etc. 

26. Find i of 1^, 2|, 3|-, etc. This work may be illus- 
trated by diagrams and is admirably suited for blackboard 
drills. 

27. Find f of ^, and extend the operation afterwards to 
„ „ integers. In getting f of 5, for example, 

I 5 3 require the following analysis: "f of 5 is the 

2 r j 3 5 I 3 same as ^ of 10, or -y-, equal to 3^. " Turn this 
"^ ^ \ finally into blackboard drills with other frac- 
■^ '^ tions. The following will illustrate: Require 

the pupils in solving the second form to say, 
" 8 times f is the same as | of 8; f of 8 is ^ of 24, or 6." 
Give many concrete examples. 

28. Train the pupils to tell instantly all the exact divi- 
sors of 6, of 8, of 10, of 12, and so on, as far as they have 
studied numbers. 

29. Ask for the least number that may be exactly divided 
by every number in each of the following groups : By 2 and 
3; 2 and 4; 2 and 5; 2, 3, and 4; 2, 3, and 6; 2, 4, and 6; 
2, 3, 4, and 6; 2, 3, 4, 6, and 12; and so on. Require a 
form of answer like the following: " The least number that 
can be exactly divided by 2, 3, 4, and 6 is 12; 12 divided by 
2 gives G; by 3, gives 4; by 4, gives 3 ; and by 6 gives 2." 

30. Train the pupils in changing groups of fractions to 
equivalent fractions having a common denominator. Thus, 
require them to change ^ and ^ to Oths, to 12ths, to 18ths, 
etc. ; 4- and \ to 4ths, 8ths, etc. ; |-, -j, f to 6ths, to 12ths, etc. ; 
i, |-, ^, f, f, f to 12ths, 24ths. These equivalences are very 
important and the children should know them as they do the 
multiplication table — without reflection or hesitation. 

31. Change fractions to simplest forms. This should be 
persisted in tmtil all the various forms of the fractions in 
common use are changed withoiit the slightest delay. Pupils 
should be able to glance down a long list of simple denomi- 
nators, decide instantly what is the least common denomi- 
nator, and then add the reduced forms as they would a col- 
umn of integers. Thus, suppose the following fractions 
were to be added: i-f ^-f | + | + | + f + | + |^^ A glance 



S 1 PEDAGOCilCS OF ARITHMETIC. 59 

should show that they must all be changed to 12ths. With- 
out writing anything, except, finally, the answer, they should 
add " 0; 4, 2, 3, 8, 9, 10, and 11." In doing this they should 
say, "0, 10, 12, 15, 23, 32, 42, 53 twelfths, or 4j\:' To 
attain to this degree of excellence will require considerable 
time, but the work should be continued until this end has 
been reached. 

32. A fractional part of an imknown number being given, 
to find the number. The following will illustrate: 

If S niaii)les are I of all the marbles that John has, how many has 
lie ? 

After many easy concrete examples, the pure number 
may be used and a blackboard drill will soon give expert- 
ness. The form of such a drill is shown below: 



8 

4 

10 

6 

13 

etc. 



^ r -, Analysis. — If | of a number is 8, i of the number 
= of ? ^ ■* 

is I of 8, or 4 ; and the number is 3 times 4, or 12. 



33. Extend the work in (32) t(~) numbers that will give a 
mixed number for the residt. Thus, 

If I of a number is 5, what is the ntimber ? 

Analysis. — If | of a number is 5, J of the number is ^ of 5, or :} ; and 
the number is 3 times |, or -^J'-, equal to Ih. 

This is suitable for drill and for concrete examples. 

34. Extend the work of (32) to such examples as the fol- 
lowing, the result being in each case an integer: 

If a boy can walk 5 miles in 1 j hours, find his rate per hour. 

Analysis. — If hours are ;; hours. If the boy can walk 5 miles 
in I hours, in i of an hour he can walk i of 5 miles, or 1 mile ; and in 
an hoi:r he can walk 3 times 1 mile, or 3 miles. 

35. Work like that in (33), the result being a mixed 
number. Thus, 

If 1| of a number is 6, what is the number ? 

Analysis. — 1| = f. If f of a number is 6, J of the number is -J- of 6, 
or I ; and the number is 3 times |, or y , equal to 3|. 



GO PEDAGOGICvS OF ARITHMETIC. § 1 

30. What part of 5 is 3 ? 

Analysis. — 1 is i of 5, and 3 is 3 times i of 5, or | of 5. 

37. Wliat part of 21 is U ? 

Analysis.— 2| = |, and 1}, — |; J is i of |; § is 3 times i of §, or 
f of |. Hence, li is § of 2J. 

The conclusion i.s stated in this example. vSome teachers 
prefer to do so in all cases. There is no serious objection 
that can be urged against the practice. 

38. What part of f is f ? 

Analysis.— | = J>^, and | = j**, ; ^i^ is J of ^%; j% is 8 times J of Z^, 
or I of j%. Hence, -| is | of |. 

39. How many times is 2^ contained in 6 ? 

Analysis. — 2', = §, and 6 = -V- ; 2|^is contained in 6 as many times 
as I is contained in y, which is as often as 5 is contained in 12, or -^^, 
equal to 2|. Hence, 21 is contained 2| times in 6. 

40. If I of I of a number is 6, what is the number ? 

Analysis. — i of ^ of a number is ^^ of it; J of ^ the number is 
2 times y*.^ of it or i of it; f of | of the number is 3 times i of it, or J of 
it. Then, if }, of a number is 6, the number is 2 times 6, or 12. Hence, 
6 is I of I of 12. 

41. How much is 5 of | of IJ ? 

Analysis.— I'of | = x*, I I o^ t = 1: f of f = 3 times |, or J. 
4 of U r= I, of § ; i of 1 = ^; i of I = 3 times ^, or |. Hence, | of f of 
iUsf. 

53. Reniai'ks on the Foregoing Selienie. — The plan 
of fraction work outlined above may seem to be a long- one, 
but, even so, it is by no means complete. These are only 
the simple fundamental operations that every person mtist 
know if he is to use fractions with any ease and effect in the 
operations of actual life. The combinations possible among 
these simple processes are nearly beyond computation. 
Still, if children are taught all these operations and are 
made thoroughly expert in them, the combinations will give 
them little trouble. 

The student will notice that every one of the types indi- 
cated above may, by the use of the simplest fractions, be 



§ 1 PEDAGOGICS OF ARITHMETIC. 61 

brought within the limits of difficulty for oral work; and, as 
has been stated, the simplest fractions are just those having 
the highest value in practice. 

It is very rarely indeed that any one is called upon to com- 
pute with sevenths or elevenths, and one is not likely, 
during the business of an entire lifetime, to be confronted 
with a calculation involving thirteenths, seventeenths, or 
nineteenths. Clearl}-, then, the teacher should lay out most 
of his effort in giving his pupils a mastery over halves, 
thirds, fourths, fifths, sixths, eighths, ninths, tenths, and 
twelfths. Of course, in the operations of addition and sub- 
traction, he must frequently reduce fractions to twelfths, 
sixteenths, eighteenths, twentieths, twenty-fourths, etc. 
These higher denominators, however, are not numerous, 
being usually such numbers as have many exact divisors, 
such as 12, 20, 24, 30, 36, 48, 72, etc. 

In seeking for a variety of good concrete examples for 
these various types, the teacher cannot do better than refer 
to the many mental arithmetics. He may be very expert in 
making examples to meet the requirements of his pupils; 
but, even so, he may get many valuable suggestions both as 
to matter and method in these useful little books. Where 
so many of them are excellent, it would be invidious to 
mention any in particular. 

With respect to the time necessary to work out the fore- 
going outline, it must not be imagined that this is a task that 
may be begun and ended within the limits of a few weeks or 
months. It should cover the entire school period in arith- 
metic, and may be repeated several times, each time witli 
more difficult numbers and new applications. If it be hur- 
ried over or be made too abstract and mechanical, it will 
become very tiresome to both teacher and pupil, and the 
result will be, in a very large measure, a failure. Above 
all, do not neglect very frequent reviews. 

54. Orig-inal Examples Made by Pupils. — No rule 
or process either in arithmetic or algebra has been thoroughly 
mastered by the pupil if he is not able to exemplify its 



62 PEDAGOGICS OF ARITHMETIC. § 1 

processes and principles by means of problems that lie himself 
has made. And this test should always be applied to him. 

The teacher may at first suggest what such an example is 
to be about. For instance, he may say : 

" You may make me an example similar to (here specify 
the example), only it must not contain the same numbers, 
and it must be about something else." Or, he may say; 

" If I knew the hourly rates of A and B, and how much 
longer A is than B in making a certain journey, I could find 
out the length of the journey. Make me such a problem." 

After some dexterity has been attained, the directions by 
the teacher may be made less and less specific. Care should 
be taken that no contradictory, absurd, or ambiguous con- 
ditions are found in these examples. They should be care- 
fully written on paper, in good English, and correctly 
punctuated. Very frequently the teacher will find some 
examples so good that he will desire to copy them into his 
note book for future u.se. 

One of the faults to be avoided is too great difficulty. 
This is a besetting sin with beginners. Pupils constructing 
original examples are likely to make some that neither they 
nor the teacher can solve. It is to be remembered that the 
chief purpose of these problems is to exemplify in each case 
some principle. If they are difficult, the principle will be 
obscured or lost in the complexity of the solution. The best 
arithmetics are, in general, the easiest. 

One other characteristic of these original problems is that 
they should be of wide variety, and yet illustrate the same 
principle and method of solution. It is wonderful how 
widely examples may sccj/i to differ and yet all belong in the 
same type. 

55. The tiearniug' of Rules and Deflnltions. — Begin- 
ners in arithmetic, as well as in nearly every other subject, 
should not be required to commit rules and principles to 
memory. These being as far as possible from the concrete, 
are utterly beyond the powers of young children. The}'^ 
have just been removed from that early domain where reality 



§ 1 PEDAGOGICS OF ARITHMETIC. G3 

is all ill all. So far they have never been required to general- 
ize or reason or discriminate or, without objective aids, to do 
any serious mental work. They have merely observed the 
qualities and activities of real things; those faculties that 
will, by and by, furnish them a very high degree of pleasure 
in dealing with pure abstractions are, as yet, dormant and 
incapable of action. Children should, at first, be shown only 
the processes; — -the liow; — the ivJiy is a matter that should 
not come until later. Require them to do again and again 
the work that will finally make them very expert in useful 
processes. When such expertness has been attained they 
may easily and gradually be led to investigate the reasons for 
their processes and to discover the involved laws and prin- 
ciples. The inductive method is the only method that can 
be successfully used with young pupils. Eveiy principle 
should be preceded by many simple exercises and problems, 
each of which contributes something towards suggesting and 
illustrating it. By the aid of many particulars, the child 
comes at length to see the general ; and, if at first he sees it 
only vaguely and dimly, there is no need for the teacher to 
worry or be discouraged. Remember that if the pupil is set 
to the task of learning principles expressed in exact scientific 
language, the effect is certain to be disastrous to mental 
growth and progress. He will surely come to hate the 
subject, and will fail to get that confidence in his own 
powers that is indispensable to real progress. In the ideal 
teaching of arithmetic, the pupil should be able to infer 
principles and to deduce rules for himself. 

5(>. Gi'apliic Illiisti'ations in Fractions. — In teaching 
fractions, the question of success turns largely on the facility 
in illustrating possessed by the teacher. In this subject of 
fractions, no point is well taught unless it is absolutely clear 
in every point. The work of graphic illustration should begin 
at the very first, and as the actual object is gradually dis- 
carded, the diagram should be the last step towards the pure 
number. Almost any simple problem in fractions may be 
solved graphically — by means of diagrams. For this purpose. 



64 



PEDAGOGICS OF ARITHMETIC. 



§1 



the square or rectangle, the circle, and the straight line may 
be used. Which is best in any given case must be determined 
by the teacher. In order to show just how this work should 
be done, a number of illustrations follow (Figs. 11 to IS): 

1. How many sixths in ^ ? 




Fig. U. 



3. What is i of J? 



jo/j^n 



#«/■# 



I of ? = I : 



4. Compare = with ^. 

2 

• ? 



Fig. 18. 



5. Divide | by |. 



t 



Fig. IJ. 



Fig. 15. 



1 — n 

3 — 15 


2 — in. 

3 — 15- 


1 — 8 
"5 — T5 


3 — 9 . 
5 — T5' 



10 _9_ -- J_ 



— T2 ~ T2 — " • "^ — 9- 



8 1 



PEDAGOGICS OF ARITHMETIC. 



G5 





S. Iff 


oi 


a certain number is 8, 


w 


hat 


i^i 


of the same number ? 








1 1 t 
1 1 




















t 

1 

9 = 

1 

1 
1 


t 


1 
i 

= 8 




1 1 1 
3 lO 4 






2 


3 -"^ < 

1 1 1 












3 


! 

4 

\ 




1 
1 

3 

\ 


1 

i 










1 
1 




1 i 1 
\ \ 1 






'1 


r 
1 

4 


t 

= 3 

\ 





Analysis. — If | of a number is 8, i of the number is \ of 8, or 4, and 
I of the number is 3 times 4, or 13; if tlie number is 12, \ of the number 
is 3, and f of the number is 3 times 3, or 9. 

7. Find % of 4. 



Fig. ir. 

fofl = |; 

2 of 4 = •3. + 24.21.2 _ 

§ of 4 = 4 times |, or |. 
8. How many times is | contained in 4 ? 



Or, 











4 
















- 1 




1 










1 








] 


r 




1 










' 








' 




^^ 






— ^ 


1^ Y 




Y 


Y 




Y 


Y 






> 



1 = I; 4 



Fk;. is. 



1X4 



\2^'l 



5*7. T^sofxil Drills iii Fractions. — Some blackboard 
drills in fractions have already been i^iven, but the extreme 
value of such exercises would seem to require that the sub- 
ject should be illustrated more fully, and that suggestions as 
to the manner of using them should accompany them. A 
very excellent method of pa-eparing these exercises is to 
mark them with a lettering brush on sheets of stiff manila 
paper about the usual size of school charts. These charts can 
then be kept for an indefinite time, especially if they are reen- 
forced by means of a flat stick above and below. Otherwise, 



66 



PEDAGOGICS OF ARITHMETIC. 



1 



they may be copied on the blackboard when required for use. 
It is very important that they shall be nsed every day once 
or oftener. The lessons should not be long, however, for it 
must be remembered that they are drills in pure number, 
and children soon weary of abstract exercises. 

There is much variety possible in the arrangement, on the 
blackboard or chart, of the inatter for drills. In general, 
the brace is very convenient for this purpose, but every 
teacher knows that children weary of sameness, and that 
they will do the same work over -many times and enjoy it as 
if it were something entirely new, provided that it is pre- 
sented to them in a new form. A circle, therefore, may be 
used for one drill, a square for another, the brace for still 
another, and so on. In the work suggested below, there is 
no intention to indicate the very best blackboard arrange- 
ment; it is the kind of work that is deemed important. 



Change : 
To 


halves. 


IS. 


To third 


S. 


To 


To fourths. 


4^ 


5i, 71 

si. 9 J 

etc. 

To sixt] 


3i, 
4|, 


5|, 
61, 
;tc. 




3f, 4>, 5| 

etc. 
twelfths. 




h h 1 
21, 3f, 4 
etc. 


1 

1 

2> 


t 


h 
1 

6> 


1. 

1 

3- 


15 3 

?' 6' ¥ 

U, H. If 

etc. 



Give analyses at first, and after a good degree of facility 
has been attained, announce rapidly results only. Rapidity 
is the end in view. Of course, the numbers must be chosen 
to suit the grade of the pupils. 

Chans^e to ones- -^7 lettering and numbering in the man- 
ner shown, no pointing is necessary, for any 
one of the 16 squares may be indicated by a 
letter joined to a number. Thus, Al means 
^; Cr^, J/; B2, J/-, etc. This same plan is 
always possible with the rectangular arrange- 
FiG. 19. ment shown in Fig. 19. 



A B C D 



23 


11 


li 
3 


22 
3 


3 


1* 

5 


la 


18 
'4 


n 

4 


1 

4 


IS 

3 


9 
7 


IS 

4 


.19 
3 


XT 

6 


S3 
6 



§1 



PEDAGOGICS OF ARITHMETIC. 



67 



5 2 3 B 7 

8' 6' 3' T' ¥' 1 i 

4 7 9 4 8 9 

3' ^' 8' ¥' T2' 12 



Find sums: 

n ! , I 9^ 41. n\.,H ^ [+\si 

71 I ] 6i 5i, 6H ^ 81 5| ^ 1 9H 

etc. J [ etc. etc. J [ etc. etc. J |^ etc. 

In doing the foreg-oing work the pupils may be instructed 
to add to 4^ each number in the second column, then to l^ 
7j, and so on down. Or, each number in turn in the first 
column may be added to 5^ in the second column, then to 9^, 
etc. Again, the pairs may be added horizontally. 

Change to 

Sixths- 1 1 S - i 11 11 21 13. 

Twelfths- I112S425SS412 

Twenty-fourths: i i, j% ^, i i, 
5 7 1 : 

Ti' 8' 12 

Change to simplest form (Fig. 20): 

A JB C J) E 

1 

2 
3 
4 

M 

Fig. 20. 
Multiply At first the pupils may find these products 

separately and then go through the formal 
addition. Thus, in finding the product of 
5| by 2, they may for a time be permitted to 
say, "Two times 5 is 10; 2 times f is |-, or 
li; 10 plus l-|-is 111. " As soon as possible, 
however, they should say only, " Two times 
5f is 10 and |, or Hi " ; " Seven times 5f is 35 and ■■y*-, or 40f. " 
Nearly all the exercises described in the general scheme of 
work in fractions may be supplemented by suitable oral 
drills, and whenever this can be done advantageously, the 
teacher shoidd prepare the drills in the best possible form. 

From what has been said about the likeness of ordinary 
integers to fractions, the teacher will, doubtless, see that 
while he is training pupils in fractions, he is training them, 



9 
i2 


8 
10 


* 

6 


IS 
24 


!•■! 
IS 




9 
IS 


6 
9 


lU 
16 


12 
16 


JO 
73 


e 

10 


.6- 

8 


8 
1* 


80 
24 


7 
14 


6 

S 


14 
94 


IX 
90 


14 
16 


JO 

le 


15 

as 


4 
IS 


14 

18 


14 

21 



H 


n] 




• 2 


81 


45 












s 


11 


8| 






'■■i 


^ by - 


3 
6 


H 


91 




4 


n 


54 J 




L7 



08 



PEDAGOGICvS OP^ ARITHMETIC. 



§1 



also, in integers. Hence, there should be no arbitrary sep- 
aration of the two — no deferring of fraction work to the time 
when the pupil has gained expertness in dealing with integers. 
It is just by this separate treatment that children are led to 
assume that there is some material difference between frac- 
tions and integers, and that they require essentially different 
methods of treatment, and, having once acquired this notion, 
they rarely, often never, get rid of it. 

58. Written Work. — The ratio of the time to be given 
to oral work in arithmetic to that which should be devoted 
to written w^ork is not constant. At first the w^ork should 
be entirely oral; but just as soon as the pupils have learned 
to write the figures and other characters used in their exer- 
cises, they should begin to do so, and to express relations 
between numbers by means of the equation. While not 
engaged in actual recitation, various forms of "busy work," 
as some one calls it, should be required of them. Otherwise, 
they are likely to find other means of being "busy " that will 
not be conducive to the best order. 

After this very early period, the written work should 
steadily increase in quantity and severity, and should consist 
less and less in purely routine mechanical operations. The 
application of the processes of arithmetic to the solution of 
practical business problems is, of course, the principal end 
in view, and to lead the pupils to make this use of the study 
is a work requiring much time and care. 

The ratio that oral and mere drill exercises should bear 
to written work combined with book work is perhaps pretty 
accurately shown in the following diagram: 

6 to 8 pears. S to 10 years. 10 to H years. 



Cr:il and Drill work. 



Written work atuljiook study 



Fig. 21. 



§ 1 peda(t()(tICvS of arithmetic. ou 

This diagram (Fig. 21) is intended to represent about the 
ages during which arithmetic is pursued in the graded schools 
of our large cities. In the country and village schools, the 
school terms are usually shorter, and the study is likely to 
be continued during the entire school life of the pupils. 



PRIMARY AVORK IX DETAIIi. 



PRELIMIXAKY OHSERVATIOXS. 

59. A Year's AVork. — There is much difference of 
opinion among writers on education as to what amount of 
number work can be well done in a year, — especially in the 
first year. After the first year the progress of pupils that 
begin together is strongly suggestive of an ordinary race in 
which there are many "starters." It soon appears that a 
few forge rapidly ahead, while all are strung out in a long 
procession. Many fall out before the goal is* reached, and 
show clearly that their powers were unequal to the require- 
ments of the struggle. It is well known that two pupils 
cannot be found whose powers are so nearly alike in kind 
and degree that they can begin and end their school work at 
the same time and with equal results. For a brief time the 
difference between them may not be appreciable, and they 
may advantageously be kept together and be under the same 
training; and, although, for reasons arising from the advan- 
tages of the division of labor, it may be best to keep them 
in the same class and under the care of the same teacher; 
yet, if it were possible, it would be better if each child cotild 
have different treatment. It is clear, therefore, that a year's 
work is, with respect to what may or should be accomplished, 
a very vague and varying expression. 

Again, there is no uniformity in the length of the school 
year. In our largest cities the usual tnne that school is in 
session is about 200 days annually, covering a period of 
ten months ; but in towns and villages the period is variable. 



70 PEDAGOGlCvS UF ARITHMETIC. § 1 

and is usually less, never more, than ten months. In country 
districts the time is rarely more than eight months, and is 
often as low as four months. Obviously, then, no definite 
amount of work could be prescribed for a general curriculum. 
The unequal capacities of children, the varied notions of what 
constitutes sufficient thoroughness in number knowledge, the 
different degrees of skill of teachers, the various methods 
employed, and many other circumstances all go to make it 
impossible to fix the amount of a year's work. And yet this 
has been attempted and has been done with the utmost 
definiteness, not only for the graded schools of large cities, 
but for schools in general. But different writers are not 
agreed on this subject, even when they assume school years 
of equal length. Many authorities think that if the subject 
be thoroughly mastered as far as 9, omitting all fractions, 
a year of ten months will be required. Others again would 
carry the work to 20 during this period, and, besides, do 
much with fractions. It is certain that no substantial agree- 
ment concerning this matter will ever be reached by the 
authorities, rror is such an agreement either necessary or 
desirable. 

60. Plan Important Ratlier tlian Amount. — The 

greatest fault to be found with the teaching of arithmetic is 
that it so often proceeds without orderly plan. Such systems 
as have been arranged and brought forward have been suc- 
cessful, not so much because of some peculiar pedagogical 
excellence as because they necessitated an orderly method of 
procedure — a sequence and gradation that made progress 
easy and rapid. At every stage of a pupil's progress there 
is always something that, logically, should come next; some- 
thing that, if it be omitted, deferred, or only partially mas- 
tered, will cause the pupil ever afterwards to proceed weakly 
and uncertainly. It is by enabling the teacher to work in 
straight lines and without wasted effort toward a definite 
object that systems of teaching arithmetic are used with so 
much advantage. The young teacher entirely without experi- 
ence needs above all things else a plan. It makes but little 



§ 1 PEDAGOGICvS OF ARITHMETIC. 71 

difference by whom it was devised, or when, provided its 
value has been proved by the test of actual trial. 

61, Every Lesson Should. Be a Iiangviage licsson. 

From the child's first day in school the work of teaching Jiim 
to express his thoughts fully and in good English should be 
begun. This is a matter of more importance than that he 
should learn arithmetic or grammar or geography ; and it is, 
besides, the most difficult task that awaits him. This lan- 
guage training can be done with special effect in the unwrit- 
ten work of the first lessons in arithmetic. During this 
early period the teacher should refuse to accept partial or 
otherwise faulty answers to questions. Thus, if the question 
were, 

"How many splints have I in my hand?" the answer 
should be, not 

" Five," but " You have five splints in your hand. " 
It is objected to this that insistence on formal exactness 
diverts the mind from the arithmetical side of the lesson and 
delays progress in the study of number. This is, doubtless, 
the case ; but it must not be forgotten that the correct, full, 
and graceful expression of thought is of more consequence 
than a knowledge of arithmetic. Moreover, the fact that 
arithmetic is one of the exact sciences would seem to require 
equal exactness in its vehicle, language. If children are 
taught from the first that careless and erroneous speech is 
not to be accepted, the necessity of interrupting them on 
that account will soon become infrequent, and correct lan- 
guage will speedily become involuntary. It is now almost 
an axiom among educators that every lesson should be a 
lesson in the correct use of language. 

63. Plan of Ti^eatnient. — One of the chief needs of 
young students of arithmetic is a good working knowledge 
and facility in the language of the subject. They should be 
carefully exercised, therefore, both in the notation and in 
the ordinary language of number. This training should 
begin with the language pertaining to oic and tzvo ; for, 



72 PEDAGOGICS OF ARITHMETIC. § 1 

while most children have a pretty good knowledge of these 
numbers, they are not able to use to any sufficient extent and 
correctly the necessary notation. The teacher must be careful 
that all answers and statements are in good English and 
complete. Nothing else should ever be accepted. 

In teaching number, the ordinal is almost as important as 
the cardinal. Frequent exercises should be had in naming 
the order of certain indicated marks or objects placed in a 
row. For example, the child should often be required to 
say such sentences as the following: "John is the first boy 
on the line." "The third figure in this number is 8." 
"Wednesday is the fourth day of the week." " Jnly is the 
seventh month of the year." In the scheme that follows, 
four matters should engage the attention witli reference to 
each number that is specially studied. 

1. The Notatnvi of the Nujiiber. 

2. The Pure {or Abstract') Number. 

3. The Applied (or Concrete) Number. 

4. The Subdivided Unit. 

The Grube method considers only the second and third of 
these phases, and yet the others are of extreme importance, 
and should not be left to incidental mention. By the sub- 
divided unit is meant that when the pupil is studying any 
integral niimber, as 3, for example, he should become 
acquainted with thirds; when he studies -i he should learn 
fourths and halves; and with G should be treated sixths, 
halves, and thirds. With these fractions should be performed 
the same fundamental operations as are common with 
integers. They are, as has been said, a kind of units as 
readily understood as any others, and their notation and 
language are very easily learned. 

63. The Niimber 1.— The important matter with refer- 
ence to this number is that pupils should understand the exact 
meaning of the language relating to it, and should acquire 
expertness in using that language. They should aLso have 
much practice on slate, paper, and blackboard in the appro- 
priate notation; in pronouncing distinctly and easily the 



§ 1 PEDAGOGICvS OF ARITHMETIC. 73 

necessary names and statements; and in recognizing and 
reading them when written in script. And in this place 
it should be remarked that children should not be required 
to imitate print, nor should the teacher attempt to make 
their tasks easier by printing lessons on the blackboard. 
From the very first, nothing but script should be used out- 
side of the textbook. The reasons for this are many and 
obvious. 

Notation.— 1 -i {\ 

U {Is, oiu\ once, jirst 

64, The ISTumber 3.— 

I. .otauon.- QQ , ..„ ]r;JtL,i| 

II. The Pure Xuniber. — 

n r 1 + 1 = 2. 

[J!2X1 = 2; 1X3 = 2. 
Measiirins: i^'ith 1. \ 

12-1 = 1. 



Q 



hi = 2. 

The task of learning to distinguish from one another, 
clearly and sharply, these four fundamental facts, and to 
understand the exact meaning of all the characters used, is 
not so easy for 3"oung children as it may seem. Much skil- 
ful questioning and many repetitions in various forms must 
be employed. The teacher that can do it quickly and thor- 
oughly may fairly be regarded as something of an artist in 
his profession. Objects that can be distinctly seen by all 
the class should be used. Questions and answers should be 
as precise as possible. Although it is assumed that under 
this head the teacher is dealing only with number in the 
abstract, there is no practical objection to having the ques- 
tions and answers contain the names of the objects (splints, 
pencils, etc.) used in the lessons. 

III. The Applied Number. — Under this head, the 
teacher must make the application of the facts taught in pure 
number. Many examples, all very simple and easy, are given 
to the class and are rapidly answered in language that, day 



74 PEDAGOGICS OF ARITHMETIC. § 1 

by day, gains in variety, correctness, and precision. Every 
example should relate to matters that lie within the experi- 
ence of the children. In no case should the teacher intro- 
duce difficulties beyond the average powers of the pupils. 
In this early teaching a puzzle of any kind should be care- 
fully avoided. A few examples involving a knowledge of 
2 are given. 

(a) Katie had 1 cent and her mamma gave her 1 cent more. How 
many had she then ? 

(d) If a pencil costs 1 cent, what do 2 pencils cost ? 

(c) Harry had 2 cherries and gave 1 of them to his sister. How 
many had he left ? 

{d) If apples are 1 cent apiece, how many apples can I buy for 
2 cents ? 

Very soon the children themselves should be called on to 
make problems like the above; and later, they will be 
delighted with telling arithmetical "stories "; that is, making 
problems answering to such expressions as 3 + 2 = , 
2x2-f 1 = , etc. 

IV. The Subdivided Unit. — As has been stated, the 
fraction is a kind of unit; the same operations may be per- 
formed upon it as upon integers. Its notation is different 
from that of units, but it is scarcely more difficult. Real 
objects, or representations of real objects, may be separated 
into parts as nearly equal as possible until the children know 
what is meant by one-half. This division should be made 
by the pupils rather than by the teacher. It must not be 
forgotten that Jialvcs of the same thing or of equal things are 
equal, and that in these exercises they should be made to 
appear as nearly equal as possible. Be very sure that the 
notation of fractions is well understood. Such expressions 
as the following should be so thoroughly taught as to be per- 
fectly easy to the children; 

- I 2 = ^ or 2. J 



ij 1 



PEDAGOGICS OF ARITHMETIC. 



75 



The teacher will notice that nothing more is to be attempted 
in fractions than is indicated above. Obviously, this traction 
work affords an excellent training in whole numbers; indeed, 
as one writer observes, if we take care of the fraction the 
integer will take care of itself. Many simple problems illus- 
trating each of the foregoing equations should be given to 
the children, and the best of these problems should be pre- 
served in a note book for future use. 

The signs -{-, — , X, -^, and = must be read with facility and 
understood as precisely as the figures and words associated 
with them. There is no general agreeinent among teachers 
about the names that, in the earliest arithmetic work, should 
be given to these signs. It is thought better by many 
teachers to defer somewhat the terms ////.s-, viiinis^ multiplied 
by, divided by, and equals or is equal ic\ and to use instead, 
and for -|-, less or take atoay for — , time or times for X, and 
is or are for =. No good substitute has been found for 
divided by, and in this fact lies an argument in favor of 
teaching at the very first the names that, sooner or later, we 
all use. Provided the children understand exactly what is 
meant hy plus, it is just as satisfactory as and, and so for the 
rest. 



65. The Xuniber 3. — 

I. Notation.— ,;, three, third, -^ | f 

-1 LI U ( t ^3 

II. Tlie Pure ]N'uniber. — Measuring and Comparing. 

f 1 + 1 + 1 = 3. 



Measuring icil/i 1. 



j\Ieasuri7ig ivith 2. 



I 3X1 = 3; 1X3 = 3. 
^ 3-1-1 = 1. 

U 13-^1 = 3. 

n n|-^-^=3; l.. = B. 

U U I 1 X 2 + 1 = 3 ; 2 X 1 + 1 =^ 3. 

n 13-3 = ,; 3-,=.. 

U L 3h-2 = 1 and 1 left (U). 



70 PEDAGOGICS OF ARITHMETIC. § 1 

Comparing. — 

3 is 1 more than 2; 3 is 3 more than 1. 

2 is 1 less than 3; 2 is 1 more than 1. 
1 is 2 less than 3; 1 is 1 less than 2. 

3 is 8 times 1 ; 1 is one-third of 3. 

1 and 1 are equal numbers ; 2 and 2 are equal numbers. 
1 and 2 are unequal (unlike) numbers ; 2 and 3 are etc. 
3 is composed of 3 equal numbers; what are they ? 
3 is composed of 2 unequal numbers ; what are they ? 

Rapid Work.— 3x1-2x1-1 = ? 3x1-1-1 = ? 
3-1-1+2=? 3-1-1-1=? 

3x1-2+1=? 1x1+1+1=? 

Note. — Much rapid oral work of this kind should be given until the 
answers can be obtained without hesitation. 

From what number can 2 times 1 be taken and 1 be left ? 

What number is 3 times 1 ? 

If one 2 is taken away from a number, 1 is left; what is the number ? 

III. The Applied Number. — 

Louis had 1 cent, his father gave him 1 cent, and he found 1 cent. 
How many cents had he then ? 

Kate had 3 apples, she atel and gave her brother 1. How many 
had she left ? 

How many cents will 3 apples cost at 1 cent each ? 

Harry had 3 pencils and lost 2 of them. How many had lie left ? 

IV. Tlie Subdivided Unit.— 

('^) J + i + i = f . or 1 ; I + 1 = I, or 1 ; i + f = §, or 1. 
{b) 3X^ = §, orl; iX3 = 1, or |. 

tr\ 3_1 — 1 — 1- ?L—'i. — \- 2_1— 1.1_2 — 1--|_1_2 
V' / 3 "3 3 — 3 ' 3 3 — 3 • 3 3 — 3 ' ^ 3 — "3 ' 3 — 3 " 

(./) 1-1 = 3; 1^1 = 3; 3 -^ t = 2; |^| = 1 and i left (H). 
{e) 1 of 3 = 1 ; I of 3 = 2 ; i of 3 = 3; 
1 = i of 3 ; 2 = 2 of 3 ; 3 = § of 3. 

RapidWork.— ix3-J = ? ^ + i-|=? l-i = ? l-§ = ? etc. 

Applied Fractions. — 

A boy divided an apple into 3 equal parts and ate 1 of the parts; 
how much did he eat, and how much was left ? 

Mary had a cherry jjie; she ate \ of it at dinner and \ of it at supper; 
how much was left ? 

What part of 3 cents is 1 cent ? 2 cents ? 

A boy had 3 marbles and lost \ of them ; how many did he lose ? 
How many were left ? 

How much less is i of a pie than | of a pie ? 



§ 1 PEDAGOGICS OF ARITHMETIC. 

GO. Tlie Xiimbei' -t. — 



77 



13 11 

4 4 ^ 



I. I^otation.— Ml '^' ^^^^^^'' f^^"''^^'^ \ I t 

II. Tlie Pure Xuniber. — Measuring and Coinparin^ 



4 

etc. 



Mcasuriiiir with 1. 



1 + 1+1 + 1=4; 1+1 = 2; 
3 + 1 = ;] ; 3+1=4. 

4X1 = 4; 1X4 = 4. 

4-1-1-1 = 1. 

4 -f- 1 =4. 



Measic?-i;i<r with 



iMeasurin^ with 3. 



OQD 

a 



2 + 2 


= 4. 


2X2 


= 4. 


4-2 


= 2. 


4h-2 


o 



8 + 1 = 4; 1+3 = 4. 

3x1 + 1=4; 1x3 + 1 = 4. 



I 4 - 3 = 1 ; 4-1=3. 

1 4--3 = 1 and 1 left (li). 
Comparing. — 
4 is 1 more than 3, 4 is 2 more than 2, 4 is 3 more than 1. 

3 is 1 less than 4, 3 is 1 more than 2, 3 is 2 more than 1. 
2 is 2 less than 4, 2 is 1 less than 3, 2 is 1 more than 1. 

1 is 3 less than 4, 1 is 2 less than 3, 1 is 1 less tlian 2. 

4 is 4 times 1, 4 is 2 times 2, 1 is ]^ of 4. 

4 is composed of 4 equal nnmbers ; what are they ? 

4 is composed of 2 equal numbers ; what are they ? 

4 is composed of 2 unequal numbers ; what are they ? 

4 is composed of 3 numbers of which 2 are equal ; what are they ? 

Rapid Work.^ 

4x1-1-1=? 4-2+1=? 4-lXl = ? 

2x2-3=? 4-T-2 4-2xl = ? etc. 

4 is the double of what number ? 

From what number must 2 be taken to have 2 left ? 

What number do I double to have 2 less than 4 ? 



Lof' 



78 PEDAGOGICS OF ARITHMETIC. § 1 

What number do I double to have 1 more than 3 ? 
Of what number is 2 the half ? Of what number is 1 the fourth ? 
How much is 1 more than one-half of 4 ? 
How much is 1 less than 2 times 2 ? 

Note. — A large number of questions like the above should be given, 
as much for the language as for the number ti-aining. 

III. The Applied Kvimber. — 

A boy had a knife with 4 blades ; he broke one of them, then another, 
and after that another. How many whole blades were there then ? 

Four birds sat on a limb; 2 of them flew away and then 1. How 
many were left ? 

Harry had 4 cents in his pocket and bought candy with I of his 
money. How much was left ? 

One orange costs 2 cents; how many oranges can I get for 4 cents ? 

A gallon is 4 quarts ; how many quarts in ^ a gallon ? 

In 1 quart there are 2 pints; how many pints in 2 quarts ? 

A boy had a gallon of milk, and sold 2 quarts of it ; how many 
quarts were left ? 

As often as Willie earns 1 dime his mother gives him 1 dime. He 
earns 2 dimes ; how many will he have then ? 

What part of a gallon is a quart ? What part of a quart is 1 jsint ? 

IV. Tlie Siibrtivided I^nit.— 

(a) t + i+-|+i = 4, or 1; 

t + t = I. orl. 

(/;) 4xi = i, orl; 1X4 = 

f,-\ 4 1 1 1 — 1. 4 3 

1 — - = 2 ■ 1 _ 1 = 3 

(,/) i^l = 4; 1-4-1 = 2; |^| = 1; | -^ f = 1 and ^ left (li); 
l-r-i=4; l--f = 2; l--f = l; 1-f-f = 1 and i left (1 J). 

{(') 1 of 4=1; I of 4 = 2; | of 4 = 3; fof4 = 4|'l = iof4; 

2 = fof 4; 3 = |of 4; 4 = |of 4. 

(/) I = !; I = I; I = i; i>i (Us greater than i); i>^; i>i. 

R(7/^l(/ Work.— iof 4 + { = ? 1-i + l = ? l + i + 1 = ? etc. 

Applied Fractions. — 

A pie was divided equally among 4 children ; what part of a whole 
pie did each child get ? 

How many fourths of an apple in 1 apple ? In i an apple ? 

If a boy pays 1 cent for 4 marbles, how much does 1 marble cost him ? 
How much do 2 marbles cost him ? 

Harry had 4 cents and gave his brother \ of them ; how many cents 
had he left ? 

. Willie lost I of his marbles ; how many did he lose if he had 4 marbles 
at first ? 



3 i_ 1 


= |, or 1; i + l 


= f, or 1 


or 1 


; fx3 = |, orl. 




1 ■ 4 


_2 — 2. 4 1 — 3. 

T — T' ¥ T — ¥' 


1 _ 3 — 1 



§1 



PEDAGOGICS OF ARITHMETIC. 



79 



In 1 gallon there are 4 quarts; how many quarts in | of a gallon ? 
In f of a gallon ? In i a gallon ? 

Katie had 1 orange ; she gave Mary | of it, and ^ of it to each of her 
2 brothers. How much had she left for herself ? 

Bessie had 4 sticks of candy and ate i of them. How many did she 
eat? 



67. The ISTunibei* 5 
I. T^otatioii. — 



( 1 1 A 92. 



II. The Pure I<"unibei* 



Measuring with 1. 



1 + 1+1+1+1 = 5; 1 + 1 --2; 
2 + 1 = 3; 3 + 1 = 4; 
4 + 1 = 5. 



Measuring with 2. 



/Measuring with 3. 



Measuring -cL'ith 4. 



5X1=5; 1X5 = 5. 
5-1-1-1-1 = 1. 

5-1 = 5. 

2 + 2 + 1 = 5. 
2X2 + 1 = 5. 
5 _ 2 - 2 = 1. 

5 -- 2 = 2 and 1 left (2i). 

3 + 2 = 5; 2 + 3 = 5. 
1X3 + 2 = 5-; 3x1+2 = 5. 
5-3 = 2; 5-2 = 3. 
5-V-8 = 1 and 2 left (1|). 





D 

QD 

00 

Q 

000 

00 
\'^' = ''- '^'-'- 

U LI U U ilx4 + l = 5; 4x1 + 1 = 5 







j 5 _ 4 = 1 ; 5-1=4. 
[ 5^4 = 1 and 1 left (1|). 



80 PEDAGOGICS OF ARITHMETIC. § 1 

Comparing. — 

5 is 1 more than 4, 5 is 2 moie than 3, 5 is 3 more than 3, 5 is 4 more 
than 1. 

4 is 1 less than 5, 1 more than 3, 2 more than 3, 3 more than 1. 
3 is 2 less than 5, 1 less than 4, 1 more than 3, 2 more than 1. 

2 is 3 less than 5, 2 less than 4, 1 less than 3, 1 more than 1. 
1 is 4 less than 5, 3 less than 4, 2 less than 3, 1 less than 2. 

5 is 5 times 1, 1 is i of 5. 

5 is 1 more than 2 times 2, 5 is 3 more than 3 times 1. 

5 is composed of 5 equal numbers ; what are they ? 

5 is composed of 2 unequal numbers ; what are they ? 

5 is composed of 3 numbers of which 2 are equal ; what are they ? 

5 is 1 more than twice what number ? 

How much more is 5 than 2 times 2 ? 

III. The Applied :Niinil)er. — 

John ate 3 chestnuts and had 2 left; how many had he at first ? 

Jane cut ofif 3 fingers of one of her gloves ; how many fingers 
were left on the glove ? 

How many quarts in 1 gallon and 1 quart ? 

Eddie went to school 3 days one week and 2 days the next week. 
How many days did he go to school in the two weeks ? 

How many yards and feet in 5 feet if there are 3 feet in 1 yard ? 

Susie had 5 cents ; she bought some candy for 1 cent and an orange 
for 2 cents. How much money had she left ? 

A father divided 5 peaches among his 3 children. He gave the 
youngest only 1 and the rest he divided equally between the other 2 
children. How many did each get ? 

How many quarts are there in 5 pints ? 

There were 5 cherries on a limb; 3 birds came and each bird took 
1 cherry. How many cherries were left ? 

IV. The Siibdi\ ided Unit.— 

('0 k+l + \ + \+l = I. oi- 1; f + 5 = i or 1; i + l = l> o^ 1; 

i + t = hovl; f + l = f, orl. 

(/;) 5 X I = I, or 1 ; I X 5 = §, or 1. 

{,-\ r>__l__l 1 1 — 1- 4_S — 1- 3__i — 2- 2 i — 1- 1 4 — 1. 

V ) 5 5 5 5 5^ — 5'5 5 — 5'5 5 — 5'5 5 5'^ 5 ^> 

1_3 _ 2- 1 2 _ .■?. 1_1 — 4 

^ 5 — 5 ' ^ 5^ — 6'^ 5 — 5- 

(,/) 5^1 = 5; i-^i = 2 andileft (3,1); f -f- f = 1 and | left (If); 
f-| = landileft(H); 1-^1 = 5; l^f = 2i; l-| = li; 1 -^ | == U. 

(c-) i of 5 = 1; fof5 = 2; | of 5 = 3; | of 5 = 4; f of 5 = 5; 
1 = 1 of 5; 2 = f of 5; 3 = f of 5; 4 = I of 5; 5 = I of 5. 

( f\ R — 4 — 3 — 2 — 1- 1^1^1<--1. l\i-^l\l 

[/ ) ^ — T— 3 — 2 — '^•5^^^3^i' 2 > -i > X > 5- 



PEDAGOGICS OF ARITHMETIC. 



81 



Rapid Work. — | x 

••^ 5 + 5 — • 5 T^ 5 5 — 



3 = ? f of 5 - 1 

-1+1 = ? etc. 



— ? 



Applied Fractions. — 

How much is left of 1 pie after eating | of the pie ? 

How many fifths of an orange in 1 orange ? 

If 5 marbles cost 1 cent, liow much will 1 marble cost ? 2 marbles ? 
3 marbles ? 

A boy picked 5 quarts of berries and spilled | of them ; how many 
quarts had he left ? 

Nellie spent \ of her money ; how much had she left if she had 5 cents 
at hrst ? 

Katy ate ^ of a pie and her brother ate ^ of it ; which ate more ? 

A boy bought 5 quarts of vinegar and spilled i of it; liow many 
quarts had he left ? 

Susie cut an orange into 5 equal parts ; she gave her brother 3 of the 
pieces and kept the rest. What part of an orange had eacli ? 

A girl was in school 5 hours one day. If | of the time was in the 
forenoon, how many hours was she there in the afternoon ? 

Tommy's papa gave him a nickel. After spending \ of it how 
much was left ? 

68. The IS^mnber 6. — 
I. Notation. — 

D Q Q D D Q ^'- ^"•' -■■••'''- * ' * ^ '* '^ 



") 2 4 6. 95 \\ 
^6 6 6 -^6 ^6 



11. Tlie Pure N^vimber, 



Q ' 



Measuring with 1. 



1+1+1+1+1+1 = 6 
1 + 1 = 3 ; 2 + 1 = 3 
3+1 = 4; 4 + 1=5 
5 + 1 = 6. 



J 6X1 = 6; 1X6 = 6. 



6-1-1-1-1-1 = 1. 



6 -- 1 = 6. 



PEDAGOGICS OF ARITHMETIC. 



Measuring with 



Measuring with 3. 



Measuring with /■. 



Meastiring with , 



DO 

QO 
DO 

DQO 
DDO 

ODOQ 
QD 

DDQDO 



2 + 242 = 6. 
3X3 = 6. 
6-2-3 = 3. 

L 6 -J- 3 ^ S. 

3 + 3 = 6. 

3X2 = 6; 2X3 = 6. 
I 6-3 = 3. 

[ 6 H- 3 = 3. 

f 4 + 2 = 6; 2 + 4 = 6. 
j 1x4 + 2 = 6; 4x1+3 = 6. 
^6-4 = 2; 6-3 = 4. 
6-4 = 1 and 2 left (If, li). 



Q 



< 



5 + 1=6; 1 + 5 = 6. 
1X5+1=6; 5x1 + 1 = 6. 
6-5 = 1; 6-1 = 5. 
[ 6--5 = 1 and 1 left (1^). 

Comparing. — 

6 is 1 more than 5, 2 more than 4, 3 more than 3, 4 more than 2, 5 more 
than 1. 

5 is 1 less than 6, 1 more than 4, 2 more than 3, 3 more than 2, 4 more 
than 1. 

4 is 2 less than 6, 1 less than 5, 1 more than 3, 2 more than 3, 3 more 
than 1. 

3 is 8 less than 6, 2 less than 5, 1 less than 4, 1 more than 2, 2 more 
than 1. 

2 is 4 less than 6, 3 less than 5, 2 less than 4, 1 less than 3, 1 more 
than 1. 

1 is 5 less than 6, 4 less than 5, 3 less than 4, 2 less than 3, 1 less 
than 2. 

6 is 6 times 1, 3 times 2, 3 times 3. 

1 is the sixth of 6, 3 is the third of 6, 3 is the half of 6. 
Of what 3 equal numbers is 6 composed ? 
Of what 2 equal numbers is 6 composed ? 
Of what 2 unequal numbers is 6 composed ? 
Of what 3 unequal numbers is 6 composed ? 



§ 1 PEDAGOGICS OF ARITHMETIC. 83 

III. Tlie Applied dumber. — 

Charles worked 3 hours at 2 cents an hour ; how much should he get ? 

There are 2 pints in 1 quart; how many pints are there in 6 quarts ? 

How many quarts are there in 1 gallon and 2 quarts ? 

A pie worth 6 cents was cut into 6 equal pieces; how much is 1 piece 
worth ? 

Six marbles were equally divided among 'S boys. How many did 
each boy get ? 

Ernest has a 2-cent piece and 2 cents. How many more cents must 
he get to have 6 cents ? 

How many apples at 2 cents each can be bought for 6 cents ? 

Mary paid 6 cents for a piece of ribbon and cut it into 2 equal 
pieces. How much should she get for one of the pieces ? 

Henry had some marbles and gave 2 of them to each of 3 boys. If 
he then had none left, how many had he at first ? 

IV. Tlio Subdivided 1 nit. — 

('^) 5 + c + g + e + g + fi = ii- »!• 1; ^ + 1 = 8. or 1; i + l = i, or 1; 
I + g = i- or 1 ; I + 

(/;) 6X^ = I, or 1; 1X6 

(C) 6 _ 1 _ 1 _ i _ 1 _ 
V"-^ « 6 6 .6 6 

((/) f--i=6; 1^1 = 3; «h-? = 2; jl--| = l and | left (1|, U); 
§-=-1 = 1 and 1 left (U); l-=-i=6; 1^,^=3; l-=-| = 2; 1-^4 

= 1}(U); 1-i = 11; 1-1 = 1. 

(6-) 1 of 6 = 1 ; ^; of 6 = 2 ; | of 6 = 3 ; | of 6 = 4 ; | of 6 = 5 ; g of 
6 = 6; 1 = 1 of 6; 2 = I of 6; 3 = I of 6; 4 = 4 of 6; 5 = I of 6; 
6 = I of 6. 

\J I 6 — 5 — T— 3 — 2— ^' U^5^?^3^3'2->a->T^5>e- 

( )r) 2 — 6 l_3.3_fi 1 — 2 2 — 4.2 — 1 t — 2 3 — 1 
y^S ' 2 6' 2 li'3 «'3 — 6'3 — B'li — ^'i; — 3'6 — 2" 

(^) i + l = i + S = I; n+l = 21; 21 + I5 = 4; etc. 
Ra/>u/ Work. — ix2 + l = ? fx3+i = ? i+|x2,= ? 
t-f + H = ? |-i + U = ? 1 + 1 + 1 = ? 1 + 1+3=? etc. 
Applied Fractions. — 

A pie was cut into 6 equal pieces and then 1 of them was eaten. 
What part of the pie was left ? 

If I of a yard of ribbon is worth 4 cents, what is i of a yard worth ? 

A boy gets 6 chestnuts for 1 cent; what does 1 chestnut cost hini ? 
What do 2 cost ? 3 ? 5 ? 

Katy had 6 apples and ate 3 of them ; what part of them did she eat ? 

Harry had an orange. He gave \ of it to his sister; how many 
sixths of it had he left ? 



1 = 


i, or 1; 


l + \ = e.orl; 


h or 


1 ■ 3 -L 3 


= i, or 1. 


1X6 


= ij, or 


1. 


1 — I 
« — r; 


• 5 4 — 
' « 6 — 


14 3 — 1.3 
« • G G G ' G 


_ 3 


.? ; 1 - ? 


= 1; 1- I =p. 



84 PEDAGOGICvS OF ARITHMETIC. § 1 

John lost i of his marbles. How many had he left, if lie had 6 at 
first ? 

A girl ate i of a pie for dinner and i of a pie for supper. How many 
sixths did she eat ? 

Louis had 6 cents and bought an orange for i of his money. How 
much had he left ? 

69. Contiuiiation of This Course. — The explanation of 
this system of elementary work has been carried far enotigh 
to show the exact plan of treatment. The teacher will 
understand that the examples given under each number 
and each subdivision are intended only to exemplify the 
method. It must not be assumed that when a teacher 
has given all these he has given all that are required. 
Innumerable problems of similar kinds to these should be 
invented, given out, and reviewed until the children can do 
very easily and rapidly what is at first done slowly and with 
difficulty. 

In the manner shown, this work should be continued up to 
and including 10, which, when thoroughly taught, is treated 
as a unit of a higher grade or order. After this point is 
reached, much of the minute detail work may be passed over 
more rapidly. For example, it is unnecessary to measure 
each number with all less numbers, and much of the compar- 
ing and combining may be oinitted. It is important that the 
children should understand exactly the relation of each num- 
ber to 10, and any of them that have exact divisors should be 
measured by using those divisors as measures. Thtis, 15 
should be measured by 3 and 5; 16 by 2, 4, and 8; 18 by 2, 
3, 6, and 9; etc. The fractional parts of these composite 
numbers should be carefully taught and frequently reviewed. 
Thus, the pupils should know without thotight or calculation 
such facts as the following: 

i i I 1 [ 2. 4. 8 li] r 3, 6 

J- of 12 = ^ 10, 3, 9 ?, i - of 15 = J 9, 13 



g, 3-, J - v.. x^ _ -^ .v., «, ^ g, g , v.. .^ _ . ^, 

hh l\ t 4, 8, 6 i, I J [5, 



10 



After reaching 20, the students should go along rapidly to 
100, by steps of 10, the important matter being that they 



§ 1 PEDAGOGICvS OF ARITHMETIC. 85 

shall be just as familiar with the order of occurrence of the 
10-groups as they are with that of the unit g'roups up to 
10. This result is attained in various ways — counting by 
units, and counting by steps of 10; as, 10, 20, 30, etc.; 
7, IT, 27, etc. ; 3, 13, 23, etc. 

The same method is pursued above 10(). From the very 
first, the children should be exercised in reading and writing 
numbers beyond those with which they work in detail. 
Thus, by the time they have finished the minute study of 
numbers as far as 10, they should be able to read and write, 
without any hesitation whatever, all numbers as high as 
100 or even beyond. 

But above all, do not neglect or abandon the work with 
fractions, and be very careful to avoid every real difficulty. 
This error of making the work too hard is just as likely to 
occur in dealing with integers as it is with fractions. 

70. The Study of Certain Coniijosite Numbers. 

After pupils have reached a certain stage of maturity, — about 
the time when they have mastered with some degree of 
thoroughness the numbers as far as 100, — it is well to study 
pretty carefully certain of the composite numbers between 
10 and 100. The reason for this is that these are the num- 
bers that must be used in adding fractions. The most use- 
ful .series is composed of the multiples of 12. They are 
24, 30, 48, GO, 72, 84, DO. For example, 24 is the least 
common denominator if we wish to add a collection of frac- 
tions containing halves, 3ds, 4ths, Gths, 8ths, 12ths, and 24ths; 
with 3(i we may add halves, ikls, 4ths, Gths, Oths, 12ths, 
18ths, and 3Gths; etc. 

Children very much enjoy the exercise of finding the com- 
ponent elements of such numbers and of changing fractions 
into equivalent fractions having a given denominator. 
Equally valuable and enjoyable is the reverse operation of 
changing fractions to simpler or to simplest forms. 

Some other numbers that are useful for the same reason 
are 20, 30, 40, 50, etc. ; 28, 32, 45, 56, etc. The number 
100 should be mastered with even greater care. Its aliquot 



86 PEDAGOGICS OF ARITHMETIC. § 1 

parts, 4, 5, 0^ 8i 10, ll^ 12|, Uf, IGf, 20, 25, 33|, and 
50, tog-ether with certain of their useful multiples, 18f, 31:^, 
37^^ 4;3|, 62i UGf, 75, 83^ and 87| should be very familiar 
to the pupils. It would not be easy to pick out a number of 
which a complete mastery would be of greater practical use- 
fulness than the number 100. 



PEDAGOGICS OF ARITHMETIC. 

(PART 2.) 



ADVANCED AVOEK. 



DEVICES AIN^D METHODS IX ADVAXCED VYOIIK. 



AnrHTION AND SI BTRAf TIOX. 

1. Addition of IjOii^ Coliimiis. — Most of the school 
exercise in addition is confined to columns of which the sum 
is less than 100, usually less than 20 or 30. Bookkeepers, 
however, are qnite frequently required to add very long col- 
umns, and it would seem to follow that the schools should 
furnish some training in such additions. For children may 
be trained to add with much expertness as far as 50 or GO, 
and yet, when required to add to higher aggregates, espe- 
cially above 100, they are slow and inaccurate. This comes 
from their lack of ability to "decimate," as some one calls 
it; that is, to pass without thought or hesitation 
from sixty sovictliing to seventy sovictJnng^ and 
the like. A good method of acquiring this ability 
is to begin to add at some number near 50, as 
shown in the margin. The large number may be 
placed either at the top or at the bottom of the column, 
according as the addition is to be upwards or downwards. 
Another plan is to add a long column two or more times 

§3 



49 


68 


8 


5 


5 


3 


7 


9 


etc. 


etc. 



2 PEDAGOGICS OF ARITHMETIC. § 2 

without returning to the beginning. In this case the sum 
will be as many times the correct result as the addition of 
the column has been repeated. 

2. Two Common Methods of Subtracting. — Teachers 
are divided in opmion as to whether it is better to diminish 
the next minuend figure after borrowing or to increase the 
next subtrahend figure. The former is the more logical 
method, but there is no doubt that the latter is the more 
convenient in practice. And since it is useless to try to 
explain to young children the reasons for either practice, it 
would seem to follow that the subtrahend figure should be 
increased. To subtract and explain by the method of dimin- 
ishing the minuend is a matter rather difficult, even for most 
young teachers. How then can children be expected to 
understand it? Suppose, for example, that the operation of 
subtracting 482,937 from 800,100, is to be explained. In 

doing so, it is necessary to 
800 100) (799(9 + 1)9(10) , /, . . ... 

4 8 2 9 3 7^/482 98 7 ^^"^^"8^® ^^® mmuend as mdi- 

„ . ^ , „ „ o 1 rr — Vl^ — W cated in the margin, in which 

olilbo ol7 lb. 3 o' 

the imits place and the thou- 
sands place are each occupied by two figures. This is a 
change that no child can be made to understand, however 
ingeniously the matter may be indicated and explained. It 
is sufficient to teach the operation without giving any atten- 
tion to the reasons. This coiu'se is frequently necessary in 
the earliest school work; indeed, it is not important or of 
any practical value that reasons for all operations should be 
perfectly known. 

In subtracting by the method of decreasing minuend 
figures, the pupils should be taught to say or think (in the 
example above) : "7 from 10 leaves 3, 3 from 9 leaves G, 
9 from 10 leaves 1, etc." All the usual long story, " 7 from 
I cannot take; I therefore borrow 1 unit from the next 
order, etc.," should be omitted. Much time can be wasted 
in trying to have this said correctly, and at the best it is the 
merest parrot exercise. Teach the process only. 

If the method preferred is to increase the figures of the 



§ 2 PEDAGOGICS OF ARITHMETIC. 3 

subtrahend, the pupils should say or think: "7 from 10 
leaves 3, 4 from 10 leaves G, 10 from 11 leaves 1, etc." Very 
soon, however, the pupils should be able to subtract faster 
than they can mention the steps in the operation, and when 
this point is reached, they should .say nothing- whatever, but 
write results as rapidly as possible. 

3. To Subtract by Adding. — An interesting and curi- 
ous question is the following: Does an unconscious addition 
precede every act of subtracting ? Do we, for example, con- 
clude that 2 taken from 7 leaves 5 only by reference to the 
fact that the sum of 2 and 5 is 7 ? Many thinkers on the 
subject believe that the mental act of subtracting is complex, 
consisting of three steps: 

1. A recognition of what is required to be done; as, that 
8 is to be taken from 15. 

2. An instantaneous judgment or recollection that the 
sum of 8 and 7 is 15, this part of the work being involuntary 
and so rapid that we are not distinctly conscious of it. 

3. The inference that 8 taken from 15 leaves 7. 
Reasoning about the matter in this way, it is urged that 

there is a gain in time and directness by omitting the third 

step, and performing the subtraction by actual addition. 

Thus, suppose we wash to subtract as in the mar- 
oQ0f)4ic) 

5 8 s Q r S '5 gin. We say only, "2 and 7 (writing 7) is 9, 
„.„„„., ^ 8 and 3 (writing 3) is 11, (carrying 1) 7 and 7 
(writing 7) is 14, (carrying 1) 10 and (writing 0) 
is 10, (carrying 1) 4 and 8 (writing 8) is 12, (carrying 1) 
and 4 (writing 4) is 13, (carrying 1)6 and 2 (writing 2) is 8. " 
Whatever may be the psychological facts back of this 
method, there is little doubt that it is the best of all in prac- 
tice, and the writer would strongly advise the student to 
make himself thoroughly expert in its use. 

4. Extension of the P^'oregoing; Method. — It is very 
frequently necessary to subtract from a given number the 
sum of several other numbers. Such an example as the fol- 
lowing requires an operation of this kind : 



4 PEDAGOGICS OF ARITHMETIC. § 3 

I had in bank 12,375.14 and drew out the following sums: 
$390.25, 1829. 08, $49.90, 1147.29, and 108.37. How much 
remained in bank ? 

Two operations seem to be necessary: (1) to 

^ ^ ^ "^ ^- ^ "^ find the sum of the subtrahends; (2) to subtract 

3 9 6.2 5 that sum from the minuend. But if the num- 

Q k^ Q /» Q 

bers be written as shown in the marg-in, the entire 
4 9 9 6 . o ' 

14 7^9 work may be done in the same manner as is 

g 8 3 7 explained in the last part of the preceding article. 
$ 8 8 3.5 9 ^® begin by finding the sum of the right-hand 
column as far as to the double line. This sum 
is 35 and the figure above is 4. We now ask what number 
added to 35 will give the least result greater than 35 that 
ends in 4. This least result is 44, and 9 is the number to be 
added. We write 9 as the first figure of the result, and carry 
4 to the next column. Carrying 4, we find the sum of the 
next column to be 26; to this we must add 5 to get 31, the 
least number greater than 26 that ends in 1. Writing 5 as 
the second figure of the answer, we carry 3 to the next 
column. The sum of the next column as far as to the double 
line is 42, and the figure 5 stands above. We now say "42 
and 3 (writing 3) is 45." Carrying 4, we obtain 29 for the 
sum of the next column, and say " 29 and 8 (writing 8) is 37. " 
Carrying 3, we get 15 for the last column, and say "15 and 
8 (writing 8) is 23." 

This operation is important because it is properly introduc- 
tory to the beautiful French Method of Long Division, an 
explanation of which will be given later. The student should 
at this point solve, in the manner explained, many examples 
in ordinary subtraction and many others like those given 
below. 



From $19,381.01 


3,109,621 


23,105,920 




' 983.47 


479,629 


13.684,789 




4,625.94 


836,784 


4,296,767 


Take ^ 


3,597.69 


39,982 


837.429 




1,426.87 


458,697 


98,765 




[ 869.96 


947,684 


9,876 



It may be observed that the only difference between this 



§ 2 PEDAGOGICS OF ARITHMETIC. 5 

operation and ordinary subtraction by the addition method 
is that in the latter case the point of departure is g-ii'fu, and 
in the former it is obtained by adding. Thus, in the first 
example above, we must add the first column as far as to the 
double line before we step across from its sum, %y^ to 4L. In 
ordinary subtraction, this preliminary addition is missing — - 
our stepping- stone or point of departure being- given. 

5. Addinji- Horizontally. — This is a method of addi- 
tion very frequently required in actual business, and yet it 
is totally neglected in our schools. The teacher should have 
frequent exercises of a kind that will render pupils just as 
rapid and accurate in adding horizontally as they are when 
the numbers to be added stand in vertical columns. There 
is really little difficulty in the matter; all that is required is 
practice. In writing the exercises, the plus sign should be 
used and the sum should be placed after the sign of equality 
in the manner shown below. 

8,329+47, 51)G + 8!)4 + (;r5,41)S + (;7 + 018 = r3;5,3:52. 
*327. (Jy + •*4-2. 1 + -*1), 47(;. 0( ) + .t3'J. 78 -|- -t 1 SO. 00 = -I? 1 (>, ( )72. 20. 

6. Addiiii*- by Groiii>s. — Any person that adds much 
comes, sooner or later, to adding by groups. At a glance he 
sees 20 in 8, 5, and 7; 18 in G, 8, and 4; and 38 in their sum. 
It soon becomes a matter of intuition to recognize the sum 
of several figures as if they were one. Beginning with 
groups of two figures, this exercise should be practiced 
until the pupil becomes proficient in it. Accountants of 
long experience add extended columns with marvelous 
rapidity, but the expertness is entirely the result of practice 
in adding by groups. If one of these expert accountants is 
questioned closely about his method, he is usually not able 
to give a very satisfactory account of it. There is one fact, 
however, that is very easily brought out. This is that he 
does not distinctly say or even think the totals obtained at 
each intermediate step; he only feels them, so to speak, but 
he relies upon the accuracy of the final result with absolute 
certainty. Having reached, say G7, he combines with it a 



C PEDAGOGICS OF ARITHMETIC. § 2 

new group of figures, whose sum is perhaps 28, with light- 
ning rapidity and without conscious effort. He does not say 
or think that 07 and 28 is 95 — he knows it without thought or 
effort, just as he knows that 2 and 3 is 5. His rapid run along 
the columns is so nearly a perfectly automatic action that the 
mental strain or exhaustion is very slight, and, like all auto- 
matic work, the result has little chance of being incorrect. 

Besides teaching mere processes to pupils, the teacher will 
do well to labor somewhat to attain this rapid, easy, auto- 
matic expcrtness, for it is not only very pleasant to do the 
work that costs us so little effort, but it is a leaven of 
expertness that makes all subsequent progress rapid and its 
results enduring. Indeed, it is well known that time neces- 
sary to make pupils thorough in fundamentals is not wasted. 

*7. Adding- Tavo or More Columns at Once. — It is 

frequently stated that expert accountants sometimes add 
several columns at once. It may be doubted whether this is 
done to any considerable extent in actual business. Of 
course, it can be done, but the necessary outlay of effort 
takes away all pleasure from the operation and the chances 
of error are much increased. 

To show the method pursued, suppose that it were required 

3 9 to add in this way the numbers in the margin. Begin- 

4 6 ning at the bottom, the successive steps are indicated 
'5 thus: 87 + 5 + 70 + (i + 40 + 9 + 30 = 247. By this 
— plan each successive step is very easy, for it is neces- 
sary to think only 87, 92, 1G2, 1C8, 208, 217, 247. In adding 
three columns, the steps are, 974, 980, 1,000, 1,400, 733 
1,489,1,492,1,512,2,212. It is scarcely necessary 8 9 
to say that practice will enable the student to 4 2 6 
perform such additions very rapidly; yet it is, no ' 
doubt, better to add each column separately. -^ -^ 1 ^ 



SHORT METHODS IX MULTIPLICATION. 

8. Proper Use of 81iort Methods. — The teaching of 
short methods to any but advanced pupils is, perhaps, 
neither wise nor necessary. With pupils of all grades the 



§ 2 PEDAGOGICS OF ARITHMETIC. 7 

shortest wa}^, provided that it is the easiest, is, of course, 
the best way; but, usually, devices intended to save time 
imply considerable expertness — more than young pupils 
have. Just in proportion as the degree of attention neces- 
sary to follow a process is increased, the ability to seize the 
involved principles is diminished. And when it is remem- 
bered that with young students the mastery of principles — 
the rationale of processes — -is the indispensable matter, it 
becomes evident that the study of short methods should be 
withheld imtil a late stage of the work in arithmetic. 

The teacher, however, should be very familiar and very 
expert with these labor-saving devices. By means of them 
he may perform very rapidly, and often without written 
Avork, examples assigned to his class. In making proljlems 
for class work, too, he may have them such as to involve 
operations that he is able to perform mentally and briefly. 
To do stich work is not only convenient in testing answers, 
but it increases the confidence of the class in their teacher 
and heightens their esteem for him. Influenced by such 
considerations the writer has deemed it best to enter some- 
what fully into this subject. 

J). ITiiAvritten Multiplication by a Multiplier of One 
Fig-lire. — It is very frequently necessary to know without 
written work such products as 9 X 37, 8 X 45, etc. In attempt- 
ing to do this "mentally," most persons try to perform the 
work as they would on slate or paper. Thus, to multiply 
37 by 9 we are likely to multiply 7 by 9, remember the 3 of 
the result, carry the 0, and unite it with 9 times 3. Th.cre 
is, however, an easier method, which is to think of 37 as 
equal to 30 + 7, multiply 30 by 9 and then add (K) to the 
priKluct. It is very easy to find the sum of a niunbcr ending 
in I) and a number of two figures, the last of which is signifi- 
cant ; as, 270 + 03, 450 -j- 81, etc. This is exactly the process 
employed in adding two or more columns at once. The 
steps necessary are illustrated below: 

40 X 5 = 300 + 30, and it is necessary to think only "2(>0, 
230." 



8 PEDAGOGICS OF ARITHMETIC. § 2 

Similarly, 
83x7 = 5G0 + -21; "500, 581," or, more briefly, "560,581." 
428X5 = 2,000 + 100 + 40; "2,000, 2,100, 2,140." 
798X6; "4,200, 4,740, 4,788." 
685x3; "1,800, 2,040, 2,055." 

10, Extension of the Forejjroiiiji: Method. — When 

both factors contain two figures, it is not so easy to do the 
work without writing, on account of the difficulty of keeping 
the figures of the factors in the mind. But if they be written, 
the multiplication is very simple by the method explained 
above. 

^^^ I ; 600, 740, 830, 851. Ijg j- ; 1,800, 2,070, 2,550, 2,622. 

If, however, one of the numbers can be separated into 
factors, it is better to multiply by the factors in succes- 
sion. 

87X45 = 87X5X0; 400, 435, 3,600, 3,870, 3,915. 

1 1 . Multipliers of Special Form. — Written multipli- 
cation may be much abbreviated in the case where the 
multiplier may be separated into groups such that one group 
is a multiple of another. Such multipliers as 936, 728, 244, 
7,212, etc. belong in this class. In the number 936, the 
groups are 9 and 36, the latter being 4 times 9; in 7,212, the 
groups are 72 and 12; in 546, they are 6 and 9 times 6; etc. 
The partial products will be as many as the number of 
groups. To show the method, let the following examples 
be taken : 

Example 1.— [Multiply 3,859 by 507; also, 432,964 by 72,364. 
Solution.— 3 8 5 9 = (J 4 3 3 9 6 4 = a 

567 7 2 3 6 4 

37013=^X7 17318 5 6=^X4 

216104 =7.^X8(0) 155867.0 4 =4.^x9(0) 

2 J g 3 Q g 3 3 1173408 = 36^? X 2(000) 

313 31006896 

If the inultiple order is reversed, the f)peration begins on 
the left. 



§ 3 PEDAGOGICS OF ARITHMETIC. 

Example 3.— Multiply 3,859 by 756; also, 433,964 by 43,673. 

Solution. — 

3859 = <? 433964 = ^ 

756 48 6 73 



3 7 18 = ax 7(00) 17 3 1856 =«X 4(0000) 
3 16 104 = TaXS 15586704 =4aX 9(00) 

29 17404 3 1173408 = 36a X 3 

18 9 08403808 

Explanation. — In the first part of example (1), we no^e 
that 507 is equal to 7, plus 80 times 7. Hence, 507 limes the 
multiplicand (which is denoted by c?) is equal to 7.7, plus 8 J 
times 7n. By writing' the second partial product one place 
to the left, the unnecessary cipher is omitted. The remain- 
ing solutions are easily understood from a brief i :spcction. 

12. Multiplication Witlioiit Partial Products. — By 

far the briefest and most useful method of multiplying one 
number by another is that in which all partial products are 
omitted. It is a favorite plan with the so called lightning 
calculators. The only difficulty it involves is the rapid and 
accurate addition of numbers containing more than one 
figure each. 

Example 1. — Multiply 43 by 56; also 67 by 54. (See diagram. Fig. 1.) 



Solution-.— 4 8 6 7 

5 4 




36 18 




Fig. L 



Explanation. — Beginning- on the right there are three 
steps in the operation. These are indicated by the symbols 
on the right. 

(a) C> times 3 = 18; write 8 and carry 1. 

(/') 1 + G times 4 + 5 times 3 = 40; write and carry 4. 

(6-) 4 + 5 times 4 = 24; write 24. 

Again, 

{a) 4 times 7 = 28 ; write 8 and carry 2. 

(/?) 2 + 4 times 6 + 5 times 7 = 01; write 1 and carry 0. 

{(•) ' + 5 times G =: 30; write 30. 



10 



PEDAGOGICS OF ARITHMETIC. 



S 2 



Most of the cases of written multiplication in actual 
business are of two figures by two figures. Hence, the 
foregoing method is of the highest practical value, and 
should be taught in the classroom. The teacher will be 
surprised at the ease with which pupils will master and use 
it. The extension of the method to numbers of more than 
three figures, while of great value to the teacher, need not 
be taught in the classroom. There is, however, no objection 
to giving it to pupils that are well advanced. 

Example ::3.— Multiply 234 by 567; also 405 by 63. (See diagram. 
Fig. 2.) 



SoLLTION. — 



2 34 
567 



40 5 
063 



132678 25515 



XXXI 

(I <■ b a 



Fig. 2. 



Explanation. — The diagram on the right indicates the 
five steps necessary to the solution, and their order is shown 
by the letters. 

[a) 7x4 = 28 ; wa'ite 8 and carry 3. 

{b) 2 + 7 X 3 + (3 X 4 = 4? ; write 7 and carry 4. 

(r) 4 + 7x2 + 5x4 + 0x3 = 56 ; write G and carry 5. 

{d) 5 + 6x2 + 5x3 = 32; write 2 and carry 3. 

{c) 3 + 5x2 r= 13; write 13. 

In the next case fill the hundreds place in the multiplier 
with a cipher, or iinagine it to be so filled, and proceed as 
before. 

{a) 3x5 = 15; write 5 and carry 1. 

{b) 1 + 3x0 + 6x5 = 31 ; write 1 and carry 3. 

{c) ;') + 3 X 4 + X 5 + 6 X — 15 ; write 5 and carry 1 . 

{d) 1 + 0x4 + 0x0 = 25 ; write 5 and carry 2. 

[c) 2 + 0x4 = 2 ; write 2. 



Example 3. 
Solution.— 



-Multiply 57,043 by 68,102. (See diagram, Fig. 3.) 



5 7 4 3 

6 8 10 2 



8884742386 



X\l/ ^S/^ ~Ai^ ^v^ \/ \/ I 
/N Wv yh-^. .-i^V /K A, I 
I /« J/ / c d c b (I 



PEDAGOGICS OF ARITHMETIC. 



11 



Explanation. — 






2x3 = G ; write G. 

2X4 + 0X3 = 8; write 8. 

2X0 + 1X3 + 0X4 = 3 ; write 3. 

2x7 + 8x3 + 0x0 + 1x4 = 42 ; write 2 and carry 4. 

4 + 2x5 + 0x3 + OX 7 + 8x4 + 1x0 = 04 ; write 4 



and carry 6. 



(/) 
carry 3 

This 



+ 0x5 + 0x4 + 1x7 + 8x0 = 37; write 7 and 



3 + 1x5 + 0X0 + 8x7 = <;4 ; write 4 and carry 6. 
+ 8x5 + 0x7 = 88 ; write 8 and carry 8. 
8 + 0x5 = 38 ; write 38. 

method is general, and, by practice, mnltiplication 
may be performed with extraordhiary rapidity. After the 
student has learned to add numbers of two figures rapidly 
and accurately, the chances of error are not so many as when 
the partial products are written and added in the usual man- 
ner. It is not necessary that the symbols be kept in mind. 
They are given above only to make the processes clearer. 
The student will notice that the operation begins on the 
right, with the first column, and advances towards the left, 
one column at each step, imtil the left-hand column is reached. 
Then the columns on the right are dropped, one with each 
step, until the last column on the left completes the opera- 
tion. The symbols picturing the operation are symmetrical 
and remind one of the development of a binomial in algebra. 
The following diagram will illustrate (Fig. 4) : 



2 flyures^ 




1 X 1 




3—, 




1 XXXI 




*___.„ 




__j XX x; X X 1 




Oi „ 


1 


V V "V^ "Sl^ ^V^ "^ V" 
/\ A\ .yS^ ViV. //V A A 


1 


1 


XX 




X X 1 



Fig. 4. 



13. Squares. — Numbers of two or three figures may 
readily be squared by utilizing the algebraic formula for the 



12 PEDAGOGICS OF ARITHMETIC. § 2 

square of a binomial — The squai'c of the sinii of t%uo quaiititics 
is equal to the square of the first, plus twiee the product of 
tJie first by the seeoud, plus the square of the second. 

Example. — Square 83 and 126. 

Solution 1.— (83)- = (80 + 3)' = 6,400 + 480 + 9 = 6,889. Ans. 
(126)= = (120 + 6)-= 14,400 + 1,440 + 36 = 15,876. Ans. 

Solution 2. — (See diagrams. Figs. 5 and 6.) 



8 3 nSn 1 2 6 



X X-X ! 



6889 ■■■■■■ 15876 



Fig. 5, Fig. 6. 

Perhaps the simplest application of thisniethod is to write 
the number but once, and then, 

(a) Square the units figure for the units figure of the 
square ; 

(/;) Take twice the product of the units and tens figures. 
The right-hand figure of this product will be the tens figure 
of the square. 

{c) Square the tens figure and write the result before the 
two figures already written. 

Of course, the necessary carrying must not be forgotten, 
and nothing but the result should be written. 

14. IMultiplier Slightly Greater or Less tliaii Some 
PoAver of lO. — It very frequently happens that one of the 
factors in multiplication is within a very few units of 100, 
1,000, or some other power of 10. Examples of such factors 
are 1»9, 908, 0095, 1,002, etc. In such cases the multiplication 
shoidd be performed by annexing the proper number of 
ciphers to the multiplicand and adding or subtracting to 
the result, as the case may require. A few examples will 
■ illustrate. 

Example 1.— Multiply 1,234 by 999. 

Solution.— 12 3 4 = 100 times 1,234 

12 34 = 1 time 1,234 

1232766= 999 times 1,234 



PEDAGOGICS OF ARITHMETIC. 



13 



Example 2.— Multiply 1,284 by 11,995. 

Soi.uiioN.— 1 2 o 4 = 10 times 1,234 



6 170 = 



5 times 1,284 



12333830=: 9995 times 1,234 

Example 3.— Multiply 3,596 by 1,003. 
Solution.— 35 9 6000 = 1000 times 3,596 



107 88= 



3 times 3,596 



3 606788 = 1003 times 3,596 

The reason for e:ieh step is so evident that no explanation 
seems to be necessary. 



15. Multiplication by Aliquot Parts. — Abbreviated 
niultipHcation by the method of aliquot parts should be per- 
fectly familiar to every teacher. It is applicable as well to 
abstract numbers as to United States money. The following- 
table shows all of these parts that are really useful in calcti- 

lation: 

Parts of One Dollar. 



.12i 
.lOf 
.25 
.331 



1 

s 




1 




1 

4 
1 
3 


' of 11. 


3 

8 





50 = i 1 



,621 = 
,6G| r= 

, 75 = 



8 I 

I \ of %\. 

'o I 



If the dollar sign be removed from the foregoing- table, the 
equality of the decimals to the abstract number 1 is shown. 
Thus, .121 or .125, = \ of 1, .1G| = i of 1, .371 or .375, 
= I of 1, etc. 

By using the fractions instead of the decimal ecjuivalents, 
multiplications (and divisions also, as will be .shown later), 
may usually be performed without written work. 

Example 1. — Find the following products ; {<i) 64 X -375 ; (/;) 68 X -875 ; 
(i-) 37X.75. 



Solution. — (a) 

Exami'LE 2. — Find the cost of 67 j^ards of carpet at §.62.} per yard. 
Solution.— 67 times §.62i- = f of $67 = ^40 + .$-'/- = §41.87.5. 



64 X .375 = f of 64 = 24. 
68 X. 875 = |of 68 = 59.5. 
37X.75 = f of 37 = 27.75. 



14 PEDAGOGICS OF ARITHMETIC. § 2 

ExAMi'LE 3. — What must be paid for 6 dozen pairs of shoes at §.66| 
per pair ? 

Solution.— 73 times §.66| = | of §72 = $48. 

16. Extension of the Foregoing- Method. — More 
useful than the foregoing table is the following extension of 
it, which will be presented under two cases. 

1. The mctJiod by iisiiii:^ multiples of tJic parts givoi in the 
foregoing tables. 

vSince %.V'l\ = i of $1, it is clear that 10 times 1. 12^, or 
11.25, - iof $10; that 112.50 is \ of 1100; and that il25 
= i of $1,000. Again, $.375 = | of $1 ; $3.75 = f of $10; 
$37.50 = I of $100; and $375 = f of $1,000. Moreover, this 
would be true if the dollar sign were removed. To show the 
application of these facts, consider the following examples: 

Example 1. — Find the cost {a) of 83 tons of hay at $13.50 a ton. 
Also, {b) of 49 tons at $13.50 a ton. 

1 ^ 

SoLUTio.N'.— (rt) A of §100 X 3)2 = $400. Ans. 

1 ^\ 

{!)) iof 6100X;=fP = §100X6^ = S<"'12..j0. Ans. 

Example 2. — What must be paid {a) for 73 acres of land, at $87.50 an 

acre ? {b) for 59 acres ? 

7 '• 

Solution.— («) ix $100X'"2 = $0,300. Ans. 

7f 
(/;) 1 X $100 X ^^f = 51 1 times $100 = $5,102.50. Ans. 

2. The method by combining the foregoing parts ivitli 
integers so as to form mixed decimals. 

Since $.121- = i of $1, $1.12^ = $1|, or $|; I2.37i = $2f, 
or $J/; $4.75 = $4|, or $-if ; etc. Obviously, the same 
equalities remain when the dollar signs are removed. 

Example 3.— Find the cost {a) of 48 yards of silk at $3.75; also, (b) 
of 39 yards at $1.87^. 

11 ^- 

SoLUTiON.— («) $-2.75X48 = $!ix^^ = $l;^2- Ans. 

47 

(b) $1.87|Xoy = $^X?^ = $00 + $!^ = $73,121. Ans. 

8 O 



16.25 


= f of *10 


8.75 


= 1 of 10 


10.25 


= V- of 10 


02.50 


=: -y- of 100 


1,025 


= y- of 1,000 


2.37i 


= ¥ of 1 



§ 2 PEDAGOGICS OF ARITHMETIC. 15 

Example 4.— Multiply {a) 1,625 by 64; also, (/;) 2,875 by 43. 

Solution. — (a) 1,625 = 1| times 1,000: 

1.-! ^ 

],(;25Xfi-l = — X 1,000 XW = 104,000. Ans. 

(/;) 2,875X43 = —X 1,000X713 = 123,r,25. Ans. 

A little practice will make the stvident qitick to sec, in each 
case, the .suitable reduction. The following- list will he found 
helpful : 

123. 75 = J/ of 110 
237.50 = -V'-of 100 
2. 121 = y- of 1 

21.25 = V- of 10 
212.50 = y- of 100 
2,125 = y- of 1,000 
2.875 = -2y of 1 
28.75 = -2^ of 10 
287.5 = -2^ of 100 
4.75 = -Y- of 1 
47.5 = J^^of 10 
475 = J/ of 100 
There arc innumerable possible reductions, which being- 
made, multiplications that seem difficult may be performed 
mentally. 

SHORT METHODS IN DIVISIOX. 

17. Division hy Aliquot Parts. — By reversing- the 
operation of multiplying by aliquot parts, a metliod is 
obtained for division by aliquot parts. This fact is illus- 
trated by the following examples: 

Example 1.— Multiply 72 by 87' and divide the product by 371. 

9 

72 V 7 V 100 
Solution.— 72x87.1 = 72 X | of 100 = - ^ ' ^ = 0,300; 

21 
G,;l00-37i = 6,300 --f of 100 = ^f^''^ ^, f = 168. 
Or, more briefly, 

70V8-1 .' ':!"i 72X7X100X8 



16 



PEDAGOGICvS OF ARITHMETIC. 



§2 



Example 2.— Divide the product of 87^ and 120 by 66| 

15 



Solution. 



120x87i-^<i6f = 



1-37.5. 



^ 2 X m 

Explanation. — Inverting the divisor, or its several fac- 
tors, the multiplication and division are performed in one 
operation. To change divisors into multipliers or multipliers 
into divisors is reversing the operation. 



To divide Ijv 



point off two deicimal 
places from 



12?r 

142 

lei 

25 

50 
371 
62 i 
661 
75 

L87i 

To divide by aliquot parts of flO or 

Since 11.25, ll.66|, $2.50, I3.33i $3.75, $G.25, $:.50, and 
18.75 are, respectively, the same part of $10 as 12^, 16f, etc. 
are of 100, we may use them as divisors in the same way as 
explained above, except that the decimal point of the result 
is moved o)ic place to the left. 

Thus, to divide $144 by $3.75: 

U4X^ 
'3 X 10 



f 8 times the dividend. 
7 times the dividend. 
6 times the dividend. 

4 times the dividend. 
3 times the dividend. 
2 times the dividend. 
% of the dividend. 
I of the dividend, 
f of the dividend. 
I of the dividend. 
I of the dividend. 

5 of the dividend. 



$144 -^$;: 



38. 4. 



Again, since $12.50, $1G.(')CI, etc. have the same ratio to 
1100 as 12^, lOf, etc. have to 100, we may proceed as above, 
and move the decimal point of the result tioo places to the 
left. 

To divide by aliquot parts of 1,000 or of $1,000. 

vSince 125, 16(;|, etc. are respectively!-, i etc. of 1,000, 
and, with the dollar sign prefixed, bear the same ratio to 
$1,000, it is evident that the method of abbreviation explained 
above applies here also, if the decimal point is moved three 
places to the left. 



§ 2 PEDAGOGICS OF ARITHMETIC. 17 

Thus, to divide I?], 905. To by ^75: 

655.25 
*l,0bi,.ro^*3<5 = i^^-j-^ = 5.242. 

In division, as in multiplication, this method may be 
extended so as to apply when any one of these aliquot parts is 
preceded by 1, 2, 3, etc. 

Thus, to find how many books at $1. 125- each may be bought 

for $45 : 

145-11.121 = i^ = 40. 

This method has been dwelt upon because of its great 
practical value, and because it is negdected in our textbooks 
on arithmetic. 

18. Divisor Slightly Less tliaii Some Po>vei' of 10. 

If a divisor is only a few units less than lOU, 1,000, etc.," 
division may be performed by a very brief and elegant 
method. 



Example 1.- 

soi.ution. — 


-Divide 492,863 by 9 

492 
2 

1 


95. 

863 

460 

1 


= 492 X 5 

= 2X5 




333 
5 


= 1X5 




qjiotient 4 9 5 


3 38 


remainder 



ExPL.ANA'JioN. — Drawing the vertical line divides by 1,000. 
But, since tlie divisor is 5 less than 1,000, the dividend is 492 
times 5, or 2,460 in excess of what it need be in order that 
995 may be contained in it 492 times with a remainder of 803, 
Dividing this excess by 1,000, the quotient is 2. Again, in this 
division the dividend, 2,4()0, was 2 times 5, or 10, greater than it 
need be, and this excess can be transferred to the remainder. 
Adding these three remainders, the sum, 1,333, will contain 
1,000 with a remainder of 333. As before, the remainder 
must be increased by 5 for each unit in the quotient; hence, 
the true remainder is 333 + '5, or 338, and the true quotient is 
equal to the sum of the several quotients, 492, 2, and 1, or 495. 



18 



PEDAGOGICS OF ARITHMETIC. 



§2 



Example 2.— Divide 23,976,428 by 9,992 (8 less than 10,000). 



Solution. — 



2397 
1 

1 



6428 

9 17 6 = 2397 X 8 

8 = 1X8 



56 12 

8 



IX 



quotient 2 3 99 5620 remainder 
Example 3.— Di\icle 5,607,496 by 96 (4 less than 100). 

Solution. — 5 6074 

2242 

89 

3 



3 



qitoticnt 5 8 4 11 



9 6 = 56074 X 4 
6 8= 2242 X 4 
5 6= 89 X 4 
1 2 = 3X4 

2 8 

j^ = 3X4 

reniaittder 



4 



The fact that examples of this kind may be very useful to 
the teacher, and that this method of solving them is not 
generally known, is the reason for introducing it here. 

Ilule. — By a vertical line, cut off on the rigJit as many 
figures of the dividend as there are figures in the divisor. 

Multiply the number on the left of this line by i^'hat the 
divisor lacks of being 100, or lf>00, etc. Write the product 
under the dividend, and if any part of this product stands on 
the left of the vertical line, continue to multiply as before 
until the product is all on the right. 

Add the numbers on the right, and if any part of the 
result falls on the left of the vertical line, multiply as before, 
and add again. 

The last sum that falls entirely on the right is the remain- 
der, and the sum of the numbers on the left is the quotient. 

19. Special Cases of tlie Foreg:oingf Metliod. — It may 

sometimes happen that the apparent remainder is greater 
than the divisor. In this case the quotient must be increased 
by 1 and the divisor subtracted from the apparent remainder 
to find the true remainder. The following examples will 
illustrate : 



s-2 



PEDAGOGICS OF ARITHMETIC. 



10 



Example 4.— Divide 641,458,207 by 9,930. Also 3,559,866 by 998. 



Solution. — (> 4 1 4 5 

449 

3 



8 2 /7 

1 5 

1 43 
2 1 



9 9 9 7 
9 9 3 



- 9930 

qitoiicnt 
?-i'i/iai/!iicr 



3559 

7 



5 ••) 7 



8 6 () -=- 998 
1 1 8 
1 4 



quotient ti 4 5 9 8 

Again it may be desired to carry out the quotient to dec- 
imal places. 

Example 5.— Divide 732,968,473 by 995, carrying the result to five 
decimal places. 

Solution.— 7 3 2 9 6 8 4 7 3 h- 995 



3664842 3 6 

188242 1 

9162 

45 



500 
180 
105 
81 
225 



820 

5 

8 2 5 remainder 



quotient 7366 5 1.73165 

Explanation. — Annex as many ciphers to the dividend 
as there are decimal places required in the quotient and 
divide as before. 

Example 6. — Divide 34,279.831 by 997 correct to four decimal places. 



Solution. — 



3427983 10 

1028394 

3085 

9 



quotient 3438 2.9799 



-^ 997 
930 
182 
255 

27 



394 
3 

3 9 7 remainder 



Explanation. — Annex four ciphers to the dividend, and 
after dividing, point off four decimal places. 

20. Divisor Slightly Greater than Some Poorer 

of 10. — In a manner very similar to the preceding method 
it is possible to divide by any number slightly greater than 



20 



PEDAGOGICS OF ARITHMETIC. 



§2 



10, 100, 1,000, etc. The only difference is that the products 
obtained by multiplying- by the excess above 10, 100, 1,000, 
etc. must be subtracted and added alternately. A few exam- 
ples will make the student familiar with the process. 

Example 1.— Divide 35,692 by 12; also 28,769,408 by 106. 
Solution. — 



{a) 


3569 

-7 13 


2- 
8 


-12 

= («) X 2 

= (/; + 1) X 2 

= (t- + l)X2 

= (^/ + 1)X2 

= (r + l)x2 

qii 
= (/)X2 
remainde}- 


(a) 

(^) 
{d) 


287694 
-17261 


8-=- 106 
6 4 = (rt) X 6 


(0 


2855 

+ 142 


4 
8 


270432 
+ 1 035 


44 

72 = (/; + l)x6 


{d) 


2998 
- 28 
2969 
+ 5 


2 
6 
6 

8 


27 1468 
62 


1 6 

1 6 = (r+l)x6 


{e) 


27 1406 
+ . 3 


00 

7 2 = (./) X 6 


(/) 


2975 
- 1 


4 

2 


27 1409 


72 

1 8 = (.') X 6 




2974 

-t- 


3 

2 


otient 


27 1409 


5 4 remainder 


quotient 


29 74 


4 





Explanation. — We shall first describe the steps of the 
process, and then indicate the reasons involved. Division by 
12 is chosen as an illustration, not because the operation is 
shorter than the usual method, but because it is long enough 
to show several repetitions of alternate adding and sub- 
tracting. 

Draw a vertical line cutting off one figure on the right of 
the dividend. This divides by 10. But the real divisor is 
12, or 2 in excess of 10. Multiply 3,569 by 2 and write the 
product with one figure to the right of the vertical line. 
Subtract this product from the number above, and note 
whether it is necessary to carry in subtracting the first 
figure after crossing the vertical line. Here, the quotient, 
3,569, is diminished by 714 instead of by 713. Multiply 
714 by 2, and writing the result as before, add it to the 
number above it. Multiply 143 by 2, and subtract the prod- 
uct from 29,982. Multiply 29 by 2 and add the product to 
29,696. So continue to multiply and then to subtract and 
add alternately until the last product stands entirely to the 



§ 2 PEDAGOGICS OF ARITHMETIC. 21 

rig"ht of the vertical Hue. The last sum or the last remainder, 
as the case may be, is the true quotient and remainder. 

The process with the example on the right is exactly 
similar, except that the vertical line cuts off two figures on 
account of the fact that, when the true divisor is lotj, the 
approximate divisor is 100. 

The reason for adding- and subtracting alternately is as 
follows : 

To divide 35,002 by 10 instead of by 12 is equivalent to 
having in the dividend 2 more than is required for each unit 
of the quotient. For the entire quotient this excess is 3,569 
times 2, or 7,138. It is clear, therefore, that the first quo- 
tient is too great, and must be diminished by 7,138-^12. 
If this deduction were made, as shown below, the result 
would be the correct quotient and remaijider. 

35G9 and 2 re;//. = 3 5 G 8 and 12 + 2, or 1 4 rem. 
7138-=-12 = 5 '■) 4 and 1 " 

Subtracting, 35(392 ^12 = 2 9 7 4 and 4 " 

But instead of doing this, we deduct 7,138-4-10, a num- 
ber too great; the difference, 2,855 -|- 4 remainder, is there- 
fore less than the correct result by (714 times 2) -=-12. 
Hence, it is necessary to increase 2,855 + 4 remainder, by 
1,428-^12. Instead of doing so, however, we increase 
2,855 + 4 remainder, by 1,428 -f- 10. This, again, being a 
deduction too great, the result is less than the true quotient, 
and must be increased. 

In this manner, we continue by turns to increase and 
diminish tlie result, approaching more and more nearly the 
correct cpiotient, until finally nothing remains to be added 
or subtracted. 

The examples chosen above do not illustrate the brevity 
of this method. They were intended to show several repe- 
titions of the alternate addition and subtraction, so that the 
student might become acquainted with the operation. If, 
however, the dividend contains only about twice as many 
figures as the divisor, the process is very brief. The follow- 
ing examples will exhibit this condition : 



22 



PEDAGOGICvS OF ARITHMETIC. 



Example 2.— Divide 8,328,967 by 10,008; also, 42,909,789 by 10,012. 
quotient 



Solution. — 



83 



8 9 6 7 
6656 



10008 



4296 
- 5 



2 3 11 remainder 



4 2 9 1 

+ 



9 7 8 9 H- 10012 
15 52 



8237 
60 



8 2 9 7 remainder 



31. Special Cases of the Foi'eg:oing;- Metliod. — There 
are two points of difficulty that may arise in using this 
method of division. They are the following- : 

(a) When the remainder contains as niaiiy figures as the 
divisor. 

In this case, one figure of the remainder would naturally 
fall to the left of the vertical line and be multiplied. By so 
continuing the operation, the correctness of the answer would 
be destroyed. This chance of error is avoided by noticing in 
each multiplication whether the product is less than the divisor. 
If it is, the operation of multiplying should not be repeated. 

(/;) Wlien in adding or subtraeting it is neeessary to 
carry 1 from the right to the left of the vertical line. 

When it is thus necessary to carry a unit across the vertical 
line, the next multiplicand must be increased by 1. If, however, 
thiscarrying occurs an even numberof times, noerrorwill arise ; 
butwithan<9rt'(r/numberof operations of carrying across the line, 
there will be error. In the first two examples in Art. 20, the 
errors would be equalized by the fact that in crossing the verti- 
cal line we carry 4 times in one example and 2 times in the other. 

The following examples will illustrate both {a) and (/;) : 

Example 3.— Divid- 317,303 by 108. Also 96,723 by 104. 

Solution. — 





3173 
- 2 5 3 


3-108 

8 4 = {a) X 8 


(0 


967 

-38 

928 

+ 1 


2 3-104 

68 = (rt)X4 


(0 


2919 
+ 20 
2939 

- 1 


1 9 

13 2 = (/; + l)X8 

5 1 q 1(0 Hi 

6 = (^) X 8 


5 5 

5 6 = (/; + l)X4 


(^) 


nit 


930 


1 1 

8 = (i- + l)X4 


quot 


2937 


9 1 

16 = (^?'+ 1)X8 
10 7 remainder 




3 remainder 



§^ 



PEDAGOGICS OF ARITHMETIC. 



33 



Example 4.— Divide 3,001,000 by 1,011; also, 89,469,212 by 1,007. 
Solution. — 



3001 
-33 



(a) 

(0 

^uo^. 2 9 6 8 



2967 



-- 1011 

01 1 = ('OX 11 
989 188842 

^2i = (/; + l)Xll {c)\+ 4 

363 
1 1 = (f + l)xll 



(a) 18946 9; 2 12 -r- 1007 
{d)\- 6 2 612 8 3 = (<t) X 7 



8884 



3 5 2 reuiainder 



929 

389 = {-^ + 1)X7 
3 18 
3 5 ■-= (6- + 1) X 7 



2 8 3 remainder 



The abbreviated method of dividing by a number sHghtly 
greater than 10, 100, 1,000, etc. is explained here only because 
of its relation to division by a number slightly less than any 
of the various powers of 10. The student should regard as 
mere curiosities such methods as have no iiseful application 
in the classroom or in actual life. They are matters that 
the teacher should k/ioio rather than attempt to use. The 
method to be exhibited next is, however, one of great utility 
and it can be applied with equal advantage to every case in 
which one integer is to be divided by another. 



33. General 3Ietlio(l of Abljreviated TjOiis Division. 

An admirable method of division is used in the schools of 
France and her colonies, and to a limited extent in other 
countries. The writer employed it for several years in a 
school containing every grade in which long division is 
taught; so that it was possible to determine with certainty 
its practical working value. The method usually employed 
in our schools was entirely discarded, and in a year or two 
after the introduction of the shorter method it was difficult 
to find a pupil tliat knew any other than that to be explained 
below. 

When the new plan was proposed, the teachers, almost 
without exception, expressed the opinion that it would prove 
too difficult for the pupils, and that a longer time and greater 
labor would be required to teach it; but when, after about 
two years' trial, they were given the option of resuming the 
old method, they were unanimous against doing so. It was 
found easier to teach, and a higher percentage of correct 



24 PEDAGOGICS OF ARITHMETIC. § 2 

results could be obtained by it than by the longer method. 
It should be stated, however, that pupils coming from other 
schools could not readily learn the new method if they 
already knew the old; but such pupils were not required to 
do so. 

It has already been stated that the best method of sub- 
tracting is by adding. This is the proper preparation for 
the abbreviated division. Logically, the next step toward 
the operation of dividing is to take away from a given 
minuend the siivi of several numbers. This is fully ex- 
plained in Art. 4, and need not be resumed at this point. 
It is Q. product and not a suvi that must be taken from the 
successive partial dividends in actual division. When the 
pupil has learned -to do this, he knows the short method of 
dividing. 

Example 1.— Divide 8,396,743 by 987. 

Solution. — di7>iso7' 8 5 7 qitoiieiit 

987)83 9 674 2 dividend 
500 
72 

3 3 3 remainder 

Explanation. — The first step is to multiply the divisor by 
the first quotient figure, 8, and subtract the product, without 
actually writing it, from the first partial dividend, 8,306. 
8 times 7 is 56, and is 56 ; W' rite and carry 5. 5 + 8 
times 8 is 60, and is 60; write and carry 6. 6 + S times 9 
is 78, and 5 is 83; \vrite 5. The remainder after the first 
partial division is 500. The next figure, 7, of the dividend 
may or may not be annexed to this, as the student prefers. 
The next quotient figure being 5, the divisor is multiplied 
by 5 and the result subtracted from 5,007. 5 times 7 is 35, 
and 2 is 37; w'rite 2 and carry 3. 3 -f 5 times 8 is 43, and 7 
is 50; write 7 and carry 5. 5 + 5 times 9 is 50, and is 50. 
The remainder is 72. The next partial dividend is 724, 
which will not contain 087. A cipher is, therefore, written 
in the quotient, another figure, 2, considered as annexed to 
724, giving 7242. In this 087 is contained 7 times. Hence, 
7 is written in the last place of the quotient and the 



§ 2 PEDAGOGICS OF ARITHMETIC. 25 

multiplication and subtraction made as before. 7 times 7 is 49 
and 3 is 52; write 3 and carry 5. 5+7 times 8 is (Jl, and 3 
is 64: write 3 and carry 6. + 7 times U is CD, and 3 is 72. 
Write 3. The final remainder is 333. 
Example 3.— Divide 123,456,7^9 by 5,4:33. 

divisor '2'2"r21 quotient 

Solution.— 5 4 3 3)133456-789 dividend 
148 1 
3953 
1503 
41 74 
3 7 3 5 remainder 

33. Division of I>eeinials. — Division of decimals is no 
more difficult than division of integers. The decimal point 
in the divisor should be moved to the right far enough to 
make the divisor a whole number, and the point in the divi- 
dend should be moved the same number of places to the 
right. The quotient should be written over the dividend, 
and its decimal point should be directly above that of the 
dividend. In moving the decimal point of the dividend it 
may be necessary to annex ciphers. 

The following examples will illustrate: 

Note.— To prevent confusion, the original position of the decimal 
point is indicated in the solution by an inverted period, while the posi- 
tion of the point after it has been changed is the same as it is usually 
printed. 

Example 3.— Divide 1.15635 by .25. 
Solution. — 4.6 2 5 

•2 5. ) M .5.6 3 5 
15 
6 

13 
Example 4. — Divide 345.6 by' 1.44. 
Solution. — 2 4 0. 

1-4 4. ) 3 4 5-6 0. 
576 

Of the methods of determining with certainty the place of 
the decimal point in the quotient, there is none qtiite .so easy 
for the pupil as that just explained. 



26 PEDAGOGICS OF ARITHMETIC. § 2 

The same method is appHcable with dollars and cents. 

Example 5. — A man bought 1.25 M shingles for $1,875. How much 
did they cost per M ? 

Solution. — $1.5 

1-2 5. ) $1-8 7.5 
625 

Example 6. — How many books at $1.75 each can be bought for $49 ? 
Solution.— 2 8. 

$1-7 5. ) $4 9-0 0. 
1 4 

Of course the teacher will understand that moving the 
decimal point in this manner is equivalent to multiplying 
both dividend and divisor by lU, 100, 1,000, etc., which has 
no effect upon the quotient. 



PROOFS OF THE FUNDAMENTAL, OPERATIONS. 

34. Proofs of Addition and Subtraction. — The pupil 
should be reqtiired to prove his work in addition by adding 
the columns in a direction opposite from the first, and in 
subtraction by showing that the sum of the subtrahend and 
remainder equals the minuend. 

35. Proofs of Miiltii>Hcation. — For beginners the best 
proof of multiplication is to multiply the multiplier by the 
multiplicand ; that is, to reverse the order of the factors. 
Somewhat later, when the pupils have mastered division, 
they may be required to show that their work is correct by 
dividing the product either by the multiplier or by the 
multiplicand. Of cour.se, this requirement should be made 
only for the sake of the practice involved, for the proof by 
this method is longer and more difficult than the original 
multiplication. 

To advanced pupils should be taught the method of proof 
by casting out O's. Since many teachers are not acquainted 
with this method, it is explained below. 



§ 2 PEDAGOGICS OF ARITHMETIC. 27 

Rule. — Add t lie digits of the multiplicand a)id tliose of the 
multiplier separately. Divide each sum by 0. Multiply the 
remainders together, and having divided the product by .9, note 
the remainder. 

Add the digits of the product and divide the sum by '■). If 
the remainder is the same as that obtained with the multipli- 
cand and multiplier, the work is probably correct. 

In case either the multiplicand or the multiplier gives 
for a remainder, the remainder for the product must be 
also. 

Illustration. — iniiltiplicaud 4 8 2 7 
multiplier 3 4 6 

product 14 9 7 14 3 

Pkook. — 4 + 3 + 2 + 7 = 10; 10^9 gives 7 remainder. 

3 + 4 + 6 = 13; 13 -^9 gives 4 remainder. 

7x4 = 28 ; 28 -=- 9 gives 1 remainder. 

1 + 4 + 9 + 7+1+4 + 2 = 28; 28h-9 gives 1 remainder. 

In using this proof it should be noted: In finding the sum 
of the digits the resulting remainder is not affected by skip- 
ping a 9 or by dropping one at any stage of the addition. 
Thus, suppose the excess of 9's in the sum of the following 
number were desired: 359,740,823. 

1. Finding the entire sum, 

3 + 5 + 9 + 7 + 4 + 6 + 8 + 2 + 3 = 47. 
Dividing by 9 ; 47 -+ 9 = 5, remainder 2. 

2. Skipping 9's, 

3 + 5 + 7 (skipping 4 + G + 8) + 2 + 3 = 20. 
Dividing by 9; 20 -=- !» = 2, remainder 2. 

3. Deducting 9 from the sum at any time during the 
addition, 3, 8, 15 (deducting 9 from 15), 6, 10 (deducting 9), 
1, 7, 15, 6, 8, 11, remainder 2. 

4. If the sum of the digits of either the multiplicand or 
the multiplier is an exact number of 9's, the same must be 
true of the prodiict. In such cases, the product of the excess 
need not be found, for it will always be 0. 



28 PEDAGOGICS OF ARITHMETIC. § 2 

To illustrate, suppose we wish to test the following: 

8343 8 + 3 + 4 + 3 = 18; ranaiudcr 0. 
5 G 2 1 



4 6 8 9 3 4 + G + 8 + 9 + G + 3 =r 30 ; rnnaindcr 0. 

5. The method fails, 

{a) when figures are transposed in the quotient; 

(//) when 9 occurs in the answer for 0, or the reverse; 

(r) when 9 or is omitted from the answer; 

{d) when a figure denotes as much too much as another 
does too little. 

It should be added, however, that none of these accidents 
is likely to happen, and that the test may usually be regarded 
as reliable. 

2(5. Proofs of Division. — There are several methods 
of proving division. Of these the best is by casting out 
9's, but this is suitable only for pupils that are pretty well 
advanced. For young pupils, the following should be 
employed : 

1. To tJic p7-oduct of tJic divisor and quotient add the 
remainder, and if the dii'ision is correct the snni will be 
equal to the dividend. 

2. Divide the dividend by the quotient, and if the quotient 
and remainder are the same, respectively, as the former 
divisor and remainder, the work is correct. 

Division by casting out 9's is proved as follows: 

3. To t lie product of the excess of 9's in the quotient and 
the divisor add the excess ofO's in the remainder. If the 
excess ofO's of this sum is the same as that of the dividend, 
the zvork may be assumed to be correct. 

To illustrate, suppose that an operation in division has the 
following elements. Is the work correct ? 

dividend 3,920,438 T dividend, 8^ 

divisor 528 ' ' j divisor, 6 i X 2 + 5 _ 

quotient 7,430 . j quotient, 2 j 9 "" ' 

remainder 230 ' [remainder, 5 J 



§ 2 PEDAGOGICvS OF ARITHMETIC. 29 

We multiply together the excess of 'J's in the quotient and 
divisor; to the product, 12, we add 5, the excess of 9's in 
the remainder, of this sum, 17, the excess of D's, 8, the same 
as in the dividend. Hence, we may assume that the work is 
correct. 



SIGNS USED IN THE FUNDAMENTAL OPERATIONS. 

27. Precedence of Signs. — There is nothing- in which 
our textbooks on arithmetic are more ambiguous than in the 
interpretation of signs. To illustrate the matter, let us 
examine the following expression : 

2x30-5x4 + = ? 

This may be interpreted in several ways, and in the 
absence of definite principles of interpretation, one result. is 
as defensible as another. For example, the operations may 
be performed in any of the following ways: 

2x30 = GO; (;0 - 5 = 55; 55x4 = 220; 220 + (> = 220. 
2x(30-5) = 2X25 = 50; 50x4 = 200; 200 + = 200. 
2X30 = 00; G0-(5X4) = 00-20 = 40; 4O + = 40. 
2x30 = GO; 00 — (5x4+0) = 00-20 = 34. 
2x(30-5) = 50; 50 X (4 + 0) = 50X10 = 500. 
2X30 = 00; 00-5 = 55; 55 X (4 + 0) = 55X10 = 550. 

Again, take the expression, 

144h-4x3-^0h-2x3 = ? 

Here we have only the signs of division and multipli- 
cation. A slight examination of this will make it clear 
that a very great nimiber of values may be found. Of 
course, all uncertainty may be removed by using symbols 
of aggregation, but these are often omitted. In order to 
lead to uniform interpretations where quantities are 
affected by several signs in sequence, some rules are 
indispensable. The following are believed to conform 
to the usage of the best authorities; biit it should be 
remembered that these principles have reference only to 
arithmetic. 



30 PEDAGOGICS OF ARITHMETIC. §2 

PKIXCIPT^KS. 

1. 1)1 fiiidi)ig the value of a sequence of uuuibers separated 
by signs of the fundamental operations, begin at the left and 
proeecd in order toivards the right. 

•I. Quantities united by symbols of aggregation must be 
redueed to a single quantity before being used as a term of the 
sequence. 

o. Multiplications must be performed before divisions., and 
both before additions and subtractions. 

•i. When some other precedence of signs or order of reduc- 
tion is intended., symbols of aggregation must be used to 
prevent ambiguity. 

Reducing" the foregoing examples in accordance with the 
principles just given: 

{a) 2x;30-5x4 + «i = 60 — -^0 + (J = 40. Ans. 

{b) 144^-4x3^0^3x3 = 144 4-12-4-6^0 = 12, 2, f 

or i Ans. 

Again, {c) (14 - 3) X 2 + 8 -^ 4 = 11x2 + 8^4 = 22+2 

= 24. Ans. 

(d) 24 - 8 X 2 + 3 X -=- = 24 - 1 -f 18 -^ = 24 - 10 + 2 

= 10. Ans. 

{e) 3X12^ 9 -0X2-=- 3X2 = 30 ^ •) - 12 -h G = 4-2 

= 2. Ans. 



(/) [42 + X 2 -^ 8 - 2 ^ 3] X 2 -^ 4 = [48 X 2 -^ H- 3] 
X2-f4 = J^x2 + 4 = U|. Ans. 



MISCELLANEOUS OPERATIONS AND SUGGESTIONS. 

38. Approximation. — Every teacher has noticed the 
fact that children in solving examples will get answers of the 
most absurd kind, and, without a suspicion of their impossi- 
ble character, await the decision of the teacher as to whether 
they are right or wrong. They never consider the question, 
" About how much should this answer be ? " Their answer 
in any given case may be a million times too great, but 
they seem to have no means of detecting it for themselves. 



§ 2 PEDAGOGICS OF ARITHMETIC. 31 

It is clear, therefore, that in this matter they should have 
specific training. There is nothing better for this pur- 
pose than exercises in what may be called appi'oxiviatioi. 
To show just what this consists in, a few examples are 
necessary. 

1. About how much is 9J times 12| ? 

Here we notice that 9J is slightly less than 10, and 12| is a little more 
than 12. Their product should therefore be about 10 times 12, or 120. 
It is, in fact, H'-'iV- 

2. What is the approximate value of 

8f X 9f X 16.^ , 
'5.9X121 ■ 

A brief examination will give something like the following as an 
approximation : 

9X10X16 
6 X 13 ' 

this reduces to 20. The true result is 19. 1 + . 
8. Find the value, ^earl3^ of 

4/riX8.125x -^'100 . 
4.0275 X 4/2T 

It is evident that we shall not be far astray by taking as an equiv- 
alent of this expression, the following: 

3X8X5 . 

~A ^ = O. 

4X0 
The correct value is 6.777+. 
4. About how much is 

20.25-6.V-K2^XlU) , 

4/19 X i'^yo 

As an approximation we may write, 

14 + 24 38 „ 

or 



4.4X4.3' 19 ~ 

The true result is 2.023+. 

5. About how much is the interest of §498.75 for 3 yr. 11 mo. 
25 d. at ^% ? 

We see at a glance that this is very nearly the same as if the 
principal were 1500 and the time 4 years, when the rate is4i-^. 



32 PEDAGOGICS OF ARITHMETIC. § 2 

Without writing anything, we say, "At 4:hfo a year, in 4 years, 
j^o of the principal equals the interest; y^g of 1500 is |90. 
Since the principal is not quite 1500 and the time is slightly 
less than 4 years, the interest must be slightly less than |90, 
say $80.50." Computation shows that the correct result is 
189. 4G+. 

The foregoing examples have been made dif^ficult in order 
to show that the method of approximating is applicable to 
every variety of problem. Before pupils are permitted to 
work out exact results, they should be required to estimate 
as nearly as possible what the answer will be. This will add 
much interest to the work, besides being of the highest 
value. Especially is this important in examples requiring 
the place of the decimal point to be determined. A friend 
of the writer speaking of this matter recently, said that 
more mistakes are made in the counting room from mis- 
placed decimal points than from any other cause, and 
added that the blunder is one that no system of double- 
entry bookkeeping will detect. "Only recently," he re- 
marked, "a Boston firm sent me a bill of $22.10 for copper; 
it should have been $221." This exercise is so important 
that it should be prescribed in the course of study of every 
school. 

29. Tlie roriniilatiiig of Operations. — Another very 
valuable exercise, which is closely related to that of approxi- 
mation, is one that may be called" /or jhh /a ting. This con- 
sists in indicating the steps necessary to the solution of 
problems. Whether or not the operation is afterwards 
actually performed is of no special consequence. Cancela- 
tion is possible in nearly all examples, and formulation, 
better than any other exercise, leads to its systematic 
use. The following exercises will illustrate the writer's 
meaning : 

Example 1. — A man walks 8| miles in 2| hours; how far at that rate 
can he walk in 4i hours ? 

84 ,, 26X24X3 
Formula.- ,1X41= ^^,^s 



§ 2 PEDAGOGICS OF ARITHMETIC. 33 

Example 2. — How much will it cost at Sl.',*5 per yard to carpet a 
room 24 X 30 feet with carpet f of a yard wide ? 

^1 o~ vx -"^ X ^0 s §5X34X80X4 
Formula.- !:,1.2a X — y— - I = 4 X 1^ X 3 ' 

E.xAMPLE 3.— What is the interest of §450 for 4 years 7 months 
at 41% 1 

. , ^ 41 , , §450 X 14 X 55 

Formula.- §450 X^X4^=.-^J^^^^^. 

Example 4. — If discounts of 40^/, 20;!, and 10?^ are allowed, what must 
be paid for a piano of which the catalogue price is §500. 

Formula.— §500 X (LOO - .40) X (1-00 - .20) X (LOO - .10) = 
§500 X .6 X .8 X .9 = §500 X .432. 

Interesting variety is added if one pupil be reqitired to for- 
mulate an example and another to perform the indicated work. 
An excellent kind of home work consists in giving a list of 
examples who.se solutions are to be indicated, but not per- 
formed. 

PROPERTIES OF XUMBERS. 

30. Divisibility of Numbers. — The teacher very fre- 
quently wishes to know whether one or more numbers may 
be exactly divided by any integer. This happens more 
especially with fractions that are, perhaps, reducible to sim- 
pler forms. The common tests of divisibility should, there- 
fore, be thoroughly familiar to the teacher, and the simplest 
and most useful of them should be carefully taught to the 
pupil. The following are of this kind : 

1. Every even iininber is exaetly divisible by 2. (Even 
numbers are such as end in 0, 2, 4, G, or 8.) 

2. If the sum of tlie digits of a number is exactly divisible 
by 3, the number itself is exaetly divisible by 3. 

Thus, 0,531 is divisible by 3, since + 5 + 3 + 1, or 15, is 
divisible by 3. The reason for this will be shown in con- 
nection wnth divisibility by 9. 

3. A number is exaetly divisible by J^ ivhen the nnndur 
expressed by its tioo right-hand figures is exaetly divisible 
byJf. 

Thus, 6,124 is divisible by 4, since 24 is divisible by 4. 



34 



PEDAGOGICS OF ARITHMETIC. 



§2 



The reason for this principle is that 100 or any multiple of 
100 is exactly divisible by 4. Now 6,124 is Gl ti'mes 100, and 
24 besides. Since 24 contains 4 exactly, it is clear that 
6,100 + 24, or 6,124, contains 4 exactly. 

4. When the last figure of a miuiber is or 5, the nninber 
is exactly divisible by 5. 

Thus, 2,170 or 3,235 is divisible by 5. For, 2,170 is 
217 times 10, and since 10 is exactly divisible by 5, it follows 
that 217 times 10 is also so divisible. Again, 3,235 is equal 
to 323 times 10, and 5 more. Now, 323 times 10, as well as 
5, is exactly divisible by 5. 

5. Any even iiuviber the sum of luhose digits may be 
exactly divided by S is exactly divisible by G. 

Thus, 3,558 is divisible by 6; for being- an even number, 
it is divisible by 2, and it is exactly divisible by 3, since the 
sum of its digits is divisible by 3. Hence, the number is 
divisible by 2 times 3, or 6. 

6. A number is exactly divisible by 8 ivhcn the number 
expressed by its three right-hand figures is exactly divisible 
by 8. 

Thus, 52,168 is divisible by 8, since 168 is so divisible. 
For, 52,168 is equal to 52 times 1,000, and 168 besides. 
Now, since 1,000 exactly contains 8, it is clear that 52,000 
does also. Hence, if 168 is a multiple of 8, the sum of 
52,000 and 168, or 52,168, is also a multiple of 8. 

7. A number is exactly divisible by 9 ivhcn the sum of 
its digits is a viultiple of 9. 

Thus, 8,451 is exactly divisible by 9, since 8 + 4 + 5 + 1, 
or 18, is exactly divisible by 9. The reasons for this may be 
seen from the following: 



,451 = 



_ J 



8000 

400 

50 

1 






999x8 + 8 

99x4 + 4 

9x5 + 5 

+ 1 



Now, since each expression under a is exactly divisible 
by 9, and since the sum of the column under b is also divisible 
by 9, it follows that the sum of a and b, or 8,451, will also 



§ 2 PEDAGOGICS OF ARITHMETIC. 35 

contain 9 exactly. It is evident that if a number is exactly 
divisible by 0, it is exactly divisible by 3. 

8. A )iu})ibcr that is exactly divisible by each of ttvo or 
more prime numbers is exactly divisible by their product. 

Thus, if 3 and 5 are each exact divisors of a number, 
15 also is an exact divisor. The same is true of 3, 7, and 21 ; 
of 2, 3, 5, and 30; of 2, 3, 7, and 42, etc. 

31. Test for Prime Numbers. — It is well known 
that there is no simple method of determining whether a 
given number is prime or not. This is imfortunate from 
the fact that it is often important to know whether a num- 
ber may be factored. Provided, however, that the number 
is not very large, the question whether or not it is prime 
may be determined without much labor, in the following 
manner: 

Suppose it is desired to test 419 for exact factors. The 
first step is to determine the approximate square root of the 
number. We see at a glance that this is between 20 and 21. 
It is clear, then, that it is necessary to ascertain whether the 
given number is exactly divisible by any number less than 21. 
If not so divisible, it is prime ; for if it has an exact divisor 
greater than 21, the quotient, which is also an exact divisor, 
must be less than 21. 

Now, it is not necessary to divide by any composite num- 
ber; for if 2 will not divide it, no multiple of 2, as 4, G, 8, etc. , 
will divide it. If 3 will not divide it, 6, 9, 12, etc. will not. 
It is clear, then, that the only divisors to be tested are the 
primes less than 21. These are 2, 3, 5, 7, 11, 13, 17, 19. Of 
these, the first five are quickly disposed of ; for at a glance, 
it is seen that neither 2, 3, nor 5 is an exact factor, and it is 
easy to try 7 and 11. They are not factors. Only 13, 17, 
and 19 remain, and but a moment is needed to try them. 
They are not divisors, and we may be certain, therefore, 
that 419 is a prime number. 

Again, let it be required to test the number 851. The 
square root of 851 being less than 30, our divisors are 2, 3, 5, 
7, 11, 13, 17, 19, 23, 29. Trying these as before, it is found 



36 PEDAGOGICS OF ARITHMETIC. § 2 

that 23 will exactly divide 851, giving a quotient 37. The 
number is, therefore, composite, and its factors are 23 
and 37. 

Once more; let us examine the number 2,257 for exact 
divisors. Our test will be confined to the prime numbers 
less than 48, for 48^ = 2,304. These numbers are 2, 3, 5, 7, 
11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. Trying these in turn, 

37 proves to be an exact divisor, and the factors are 37 
and Gl. 

In the case of large numbers, this method is somewhat 
tedious, but it is the only one available, and pupils should 
know how to apply it. Besides some other advantages, it 
involves valuable practice in division. 

33. Prime Xuinbers. — Teachers should see to it that 

pupils are very familiar with all prime numbers within the 
upper limit of the multiplication table; that is, as far as 139, 
or higher. Omitting 1, these primes are, 2, 3, 5, 7, 11, 13, 
17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 
89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139. 

315. Table of Prime Numbers.- — For purposes of ref- 
erence the following table of all the prime numbers less than 
0,000 will be found useful in the classroom. One of the most 
important applications of the table is to tell at a glance 
whether a given fraction is in its simplest form. Knowing 
that a fraction cannot be .simplified if either of its terms is a 
prime number, a mere glance at the table will often save 
the operation of finding their greatest common divisor. Of 
course, the terms may be prime to each other, and yet both 
be composite numbers, and the fraction be, therefore, irre- 
ducible to lower terms. In this case, the greatest common 
divisor test must be applied. 

To use the table, look for the thousands figure above one 
of the divisions of the table. Then, under the thousands 
figure, find the hundreds figure at the top of one of the ten 
columns. If the number is prime, the remainder of the 
number will be found below in this column. 



8 2 



PEDAGOGICS OF ARITHMETIC. 



37 



PRIME NUMBERS. 






1 


2 


o 


I 


2 


3 


4 


5 


6 


7 


8 


9 





I 


2 


3 


4 


5 


6 


7 


8 


9 





I 


2 


3 


4 


5 


6 


7 


8 


9 


I 


OI 


II 


07 


01 


03 


01 


01 


09 


07 


09 


03 


01 


01 


09 


II 


01 


09 


01 


01 


03 


II 


03 


09 


II 


03 


09 


07 


01 


03 


2 


oy 


23 


II 


09 


09 


07 


09 


II 


II 


13 


09 


13 


03 


23 


23 


07 


21 


II 


07: 


II 


13 


07 


II 


17 


21 


17 


II 


03 


09 


3 


07 


27 


13 


19 


21 


13 


19 


21 


191 


19 


17 


17 


07 


27 


31 


09 


23 


23 


13 


17 


29 


13 


33 


23 


31 


21 


13 


19 


17 


5 


09 


29 


17 


21 


23 


17 


27 


23 


29 


21 


23 


23 


19 


29 


43 


13 


33 


31 


31' 


27 


31 


21 


39 


37 


39 


33 


19 


33 


27 


7 


13 


33 


31 


31 


41 


19 


33 


27 


37; 


31 


29 


29 


21 


33 


49 


19 


41 


47 


33, 


29 


37 


37 


41 


41 


43 


47 


29 


37 


39 


II 


27 


39 


37 


33 


47 


31 


39 


29 


41 


33 


51 


31 


27 


39 


53 


21 


47 


bi 


49 


39 


41 


39 


47 


47 


49 


57 


31 


43 


53 


13 


31 


41 


47 


39 


57 


41 


43 


39 


47i 


39 


53 


37 


bi 


47 


59 


27 


53 


07 


51: 


53 


43 


43 


51 


59 


51 


59 


41 


51 


57 


17 


37 


51 


49 


43 


b3 


43 


51 


53 


53 


49 


(>3 


49 


67 


51 


67 


37 


59 


71 


73 


63 


53 


51 


57 


07 


57 


63 


49 


57 


63 


19 


39 


57 


53 


49 


69 


47 


57 


57 


67 


51 


71 


59 


73 


53 


71 


57 


77 


73 


79 


69 


bi 


b7 


71 


73 


79 


71 


53 


bi 


69 


23 


49 


63 


59 


57 


71 


53 


()i 


59 


71 


61 


81 


77 


81 


59 


79 


63 


83 


77 


87 


Si 


79 


69 


77 


77 


91 


77 


67 


79 


71 


29 


51 


69 


^7 


61 


77 


59 


69 


63 


77 


63 


87 


79 


99 


71 


83 


67 


87 


79 


93 


83 




73 


81 




93 


83 


77 


87 


99 


31 


57 


71 


73 


63 


87 


61 


73 


77 


83 


69 


93 


83 




81 


97 


69 


89 


89 


97 


87 




81 


83 






87 


89 


97 




37 


63 


77 


79 


67 


93 


73 


87 


81 


91 


87 




89 




83 




93 






99 


89 




87 


89 






89 


91 






41 


67 


Si 


83 


79 


99 


77 


97 


83 


97 


gr 




91 




87 




97 








99 




93 


93 






93 


97 






43 


73 


83 


89 


87 




83 




87 




93 




97 




89 




99 












97 


99 






99 








47 


79 


93 


97 


91 




91 








97 








93 
































53 


81 






99 




















99 
































59 


91 


























































6 1 


93 


























































^1 


97 


























































71 


99 


























































73 




























































79 




























































83 






















' 






































89 




























































97 





























































3 


4 








5 





I 


2 


3 


4 


5 


6 


7 


8 


9 





I 


2 


3 


4 


5 


6 


7 


8 


9 





I 


2 


3 


4 


5 


6 


7 


8 


9 


01 


09 


03 


01 


07 


II 


07 


01 


03 


07 


01 


II 


01 


27 


09 


07 


03 


03 


01 


03 


03 


01 


09 


03 


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01 


23 


01 


01 


03 


II 


19 


09 


07 


13 


17 


13 


09 


21 


II 


03 


27 


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37 


21 


13 


21 


21 


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09 


09 


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27 


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0; 


39 


II 


07 


23 


19 


21 


17 


13 


33 


27 


17 


19 


23 


17' 


07 


29 


17 


39 


23 


17 


37 


23 


17 


19 


II 


13 


31 


23 


17 


07 


41 


17 


n 


27 


23 


37 


21 


19 


49 


29 


23 


27 


33 


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13 


33 


19 


49 


41 


19 


39 


29 


31 


31 


21 


19 


33 


33 


19 


19 


47 


37 


21 


39 


37 


63 


29 


23 


57 


33 


31 


33 


47 


23 


19 


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29 


57 


47 


23 


43 


33 


bi 


33 


23 


47 


37 


47 


31 


21 


51 


41 


27 


53 


41 


67 


51 


29 


61 


39 


37 


39 


51 


29 


21 


53 


31 


63 


51 


47 


49 


51 


71 


37 


39 


53 


bi 


51 


37 


27 


53 


43 


39 


Si 


49 


69 


53 


31 


63 


41 


43 


bi 


53 


31 


27 


57 


41 


73 


57 


49 


51 


59 


77 


43 


51 


67 


73 


Si 


41 


31 


57 


49 


43 


87 


61 


Si 


57 


43 


67 


47 


59 


67 


63 


43 


49 


59 


43 


91 


63 


61 


57 


83 


89 


51 


59 


71 


79 


87 


43 


57 


59 


79 


49 




67 


87 


59 


47 


69 


57 


71 


69 


77 


47 


51 


77 


53 


97 


Si 


67 


63 


87 




57 


77 


79 


Si 


93 


49 


63 


69 


83 


51 




79 


91 


71 


59 


91 


59 


73 


79 


Si 


67 


57 




59 




83 


83 


73 


89 




67 


81 


89 


97 


99 


71 


69 


83 


91 


57 




83 




99 


61 


99 


71 


77 


93 


89 


89 


73 




61 




93 


91 


79 


93 




69 


87 


97 






77 


73 


89 




bi 




89 






71 
73 
89 
91 




Si 
83 
93 


91 

97 


97 






79 
91 
93 
99 




71 
73 
83 
89 
97 






97 


91 


99 




73 
87 
93 
99 


99 








79 

83 


Si 
91 


93 




67 
69 
79 
Si 

97 





38 PEDAGOGICvS OF ARITHMETIC. 



FACTOKS, DIVISORS, AISTD MUI.TIPLES. 

34. Faetoriiij^. — In arithmetic, as in algebra, the expert- 
ness of pupils depends very much on their skill in factoring. 
Nearly all operations involve cancelation, and skill in this 
requires that the pupil shall be quick in recognizing the fac- 
tors of numbers. The subject of factoring and its various 
applications should be carefully taught. It will be found of 
great assistance in this work to have pupils leani the multi- 
plication table farther than the usual limit, 12 times 12. A 
few minutes' work each day for a few weeks will enable them 
to accomplish this task, and they will then have not only 
much added skill in factoring numbers, but a contribution to 
practical efficiency that will be of extreme value during all 
their future life. 

In resolving any number into factors pupils should be 
taught that the work is not completely done unless the result- 
ing factors are all prime numbers. Thus, the factors of 60 
are not and 10, or 12 and 5, but 2, 2, 3, and 5. 

The operation of finding these factors by division should 
begin with the least prime number that is an exact divisor. 
The division of the number and each successive quotient by 
this divisor should be continued as long as possible. The 
next greater prime number should be used in like man- 
ner, until the last quotient is prime. All these successive 
divisors and the last quotient are together the required prime 
factors. To illustrate, let it be required to find the prime 
factors of 34,650. 

. „ ^ „ Hence, the prime factors of 34,650 are 2, 3, 3, 

\ „ 3 'I ^ 5, 5, 7, 11; or, 34,050 = 2X3^X5^X7X11. This 

^ r. r. r result may be written 2. 3". 5^ 7.11. For small 
5 7 7 5 •' 

„ g ^ numbers the factors may be written out at once, 

r-r-- the divisions being performed mentally. Thus, to 

find the prime factors of 120, we may say, "120 



< i 



~ divided by 2 (write 2) is 60; 60 divided by 2 (write 
2) is 30; 30 divided by 2 (write 2) is 1 5 ; 15 divided 
by 3 (write 3) is 5 (write 5). The prime factors are, there- 
fore, 2, 2, 2, 3, 5; or, 120 = 213.5." 



§ 2 PEDAGOGICS OF ARITHMETIC. 39 

35. Greatest Coiiiniou Divisor by Factoring'. — With 
numbers within the range of the ordinary multiplication 
table, pupils should have no difficulty in determining the 
greatest common divisor by inspection. At any rate, they 
should be trained until they can do so. A good practical 
form of this exercise is in simplifying such fractions as |^|, 
36^ ||.^ etc. When the pupils have become proficient in doing 
this, larger numbers may be used, and the method l)y factor- 
ing employed. Thus, such fractions as the following may 
he taken- ^.ai 5.12. 5.0.4 gf^ 

In simplifying such fractious, the work may be advan- 
tageously performed in such manner as to make the pupils 
familiar with various ways of indicating products. 

433 ^ 2X3X2X2X3X3X3 
768 3X2X3X3X3X3X3X3X3 

_ 3^ X 3^ _ (2\^yxn- __ ^ _ ^ 

~ 3^X3 ~ (3\3)X3^ "■ 3"^ ~ 16 

504 ^ 3 X3X3X3X3X 7 ^ 3^ X 3^ X 7 ^ (3l3'0x3x7 ^ 14 
540 2X3X3X3X3X5 3^ X 3--' X 5 (3^3--') X 3 X 5 15 

The important matter at this stage is not to get the 
simplest form of the fraction in the briefest possible way, 
but to reveal the principles involved in the operation. The 
pupils should be questioned about the work, and should be 
required to find the greatest common divisor of the terms 
by multiplying together the common prime factors. In the 
first example above, this greatest common divisor is 2\o, or 
48; in the second, it is 2". 3", or 30. By being required to 
reduce the fractions at one division of their terms, the pupils 
will understand the purpose of finding the greatest common 
divisor. This is especially important where the greatest 
common divisor must be found by the process of division. 

Thus, 

433 --3\3 _ 432 --48 _ 9^ 
768 -f- 2^3 ~ 768--48 " T6' 
504-4-2^3- _ 504 -=-36 _ 14 
540 --2^3- ~ 540-^36 ~ 15' 

The method of finding the greatest commcjn divisor by 
factoring is sufficient for nearly all practical needs ; but it is 



40 PEDAGOGICS OF ARITHMETIC. § 2 

occasionally necessary to resort to the method by division. 
The pupils should understand this method and the principles 
on which it depends. These principles are the following: 

1. A /I exact divisor of a number is an exaet divisor of any 
multiple of that nnmber. 

Thus, 7, being an exact divisor of 14, is an exact divisor of 
2 times 14, o times 14, etc. For, since 7 is contained 2 times 
in 14, it is contained 2 times X2, or 4 times, in 14x2; it is 
contained 2 times X 3, or G times, in 14x3; etc. 

2. An exact common divisor of two numbers is an exact 
divisor of their sum. 

Thus, since 7 is an exact divisor of 14 and 35, it is an 
exact divisor of 14 + 35, or 40. For, 7 is contained in 
14, 2 times, and in 35, 5 times; hence, 7 is contained in 

14 + 35, 2 times +5 times, or 7 times. 

3. An exaet common divisor of tivo numbers is an exact 
common divisor of their difference. 

Thus, since 7 is an exact common divisor of G3 and 35, 
it is an exact common divisor of G3 — 35, or 28. For, 7 is 
contained in G3, 9 times, and in 35, 5 times; hence, 7 is con- 
tained in 63 — 35, 9 times — 5 times, or 4 times. 

4. An exact common divisor of two numbers is a)i exact 
common divisor of the sum of any multiples of those 
numbers. 

Thus, since 7 is an exact common divisor of 21 and 35, it 
is an exact common divisor of 21x5 + 35x4. For, .since 
7 is contained 3 times in 21, it is contained 3 times X 5, or 

15 times, in 21 X 5; and, since 7 is contained 5 times in 35, 
it is contained 5 times X 4, or 20 times, in 35x4. Hence, 
7 is contained 15 times +20 times, or 35 times, in 
21X5 + 35X4. 

5. An exact connnon divisor of two numbers is an exaet 
common divisor of the difference between any multiples of 
those n7i7nbers. 

Thus, since 7 is an exact common divisor of 28 and of 35, 
it is an exact common divisor of 28 X G — 35 X 3. For, 
since 7 is contained 4 times in 28, it is contained 4 times X G, 
or 24 times, in 28 XG; also, since 7 is contained 5 times 



§ 2 PEDAGOGICS OF ARITHMETIC. 41 

in 35, it is contained 5 times X 3, or 15 times, in 35x3. 
Hence, 7 is contained 24 times — 15 times, or 9 times, 
in 28 X 6 - 35 X 3. 

The following illnstration will enable the student to see 
how these principles apply in finding the greatest common 
divisor of two numbers. Let us take 15 X 29 and 47 X 29, or 
435 and 1,363. Here, we know in advance that the greatest 
common divisor is 29. 

Explanation. — By principle 1, we know that since 29 is 

a divisor of 15x29 it is a divisor of 3 times 15x29, or 

15X29)47X39(3 45 times 29. By princi- 

4 5x29 pie 5, 29 is a divisor of 

3X39)15X29(7 47 X 29 - 45 X 29, or 

^^X^^ 2 X 29. These two prin- 

1X^«>)'-X~9(3 ciples account for every 

3X29 

other step in the proc- 
ess until the last difference of multiples, 1 X 29, turns out to 
be an exact divisor of the preceding difference of multiples, 
2 X 29. But, since no divisor of 1 X 29 can be greater than 
29, it is evident that the last divisor, 29, is the greatest com- 
mon divisor sought. 

Let us take now two numbers whose greatest common 
divisor is hidden in the numbers. 
Solution.— 136 5)339 5(3 
8730 
6 6 5)1365(3 
13 3 

35)66 5 ( 1 9 
3 5 
3 1 5 
315 

Explanation. — The greater number is divided by the less, 
the less by the first remainder, the first remainder by the 
second remainder, and so on, until, finally, the greatest 
common divisor, 35, appears as an exact divisor of the pre- 
ceding remainder. 

36. Apj)lication of Abbreviated Division. — The 

short method of division already explained may be advan- 



42 



PEDAGOGICS OF ARITHMETIC. 



§3 



tageously applied to finding the greatest common divisor of 
two numbers. To show this, both methods are given below 
side by side. 

Example 1. — Find the greatest common divisor of 437 and 943. 

Solution. — 



437)943(3 

874 



9 



437(6 
4 1 4 



437 


94 3 


23 


69 








S3 



69(3 
69 



Example 2. — Find the greatest common divisor of 2,358 and 10,728. 
Solution. — qtioticnis quotients 



2358)10728(4 
9432 



12 9 6)2358(1 
1 2 9 6 

10 6 2)1296(1 
1062 



1 


2 3.58 


10728 


4 


1062 


1296 


1 


1 26 


234 




IS 


1 08 




2 3 4)1062(4 
936 



126)234(1 
1 26 



10 8)126(1 
1 08 
18)108(6 
1 08 

Example. — Find the greatest common divisor of 2,431 and 12,259; 
also, of 9,711 and 38,761. 
quotients quotients quotients 



23 


2431 


12259 




35 


1 04 


1 


3 9 


26 




13 






97 11 


38761 


83 


9628 




1 3 




49 



quotients 
3 
1 16 



37. Ijeast Common Multiple by Factoring. — Few 

pupils understand, at least until late in their school course, 
the exact nature of the least common multiple of two or 
more numbers. And yet the operation is of much importance 
since it must frequently be resorted to in adding or subtract- 
in<i' fractions. 



§ 2 PEDAGOGICS OF ARITHMETIC. 43 

The neatest method of finding the least number that each 
of several numbers will exactly divide is by factoring. 
This, with the explanation, will now be given. 

Example 1. — Find the least common multiple of 24, 42, 54, and (50. 

Solution. — 24 = 2^3 

42 — 2 3 7 

^-^^ 2^315.7 = 7.5G0 = L. CM. 

GO = 2-. 3. 5 

Explanation. — A number to be exactly divisible by 24 
must contain the factors of 24, or 2\3; to be divisible by 
both 24 and 42, it must contain 2^3.7, a combination in 
r 03 3 = 3-i 5 7 = 315 which each set of factors 

' 2.3.7 = 2\3'-'.5 = 180 may be found complete; to 
^'■'^'■'^■'"^ j ~'.3^ = 2%5.7 = 140 be divisible by 24, 42, and 

I 2". 3.5 = 2.3-. < = 12() -j^^ j|. j-f-^^^^i- contain the fac- 
tors 2''. 3''. 7; to be divisible by 24, 42, 54, and GO, it must con- 
tain the factors 2\ 31 5. 7. If this last set of factors, 21 3^ 5. 7, 
be divided in turn by the set of prime factors representing 
each number, the results will be as shown in the margin. 

A consideration of the foregoing enables us to deduce the 
following principles: 

1. Tlic least common multiple of tivo or viore numbers con- 
tains all the prime factors of each of the numbers considered 
separately, and it contains no other factors. 

2. Each prime factor occurs in the least common multiple 
as many times as it occurs in the number that contains it the 
greatest number of times. 

The student should notice that this method requires all 
factors to be prime. A distinct pedagogical advantage 
arising from the method by factoring is that both the 
greatest common divisor and the least common multiple of 
two or more numbers are easily derived directly from their 
factors. 

Example 2. — By the method of factoring find the greatest common 
divisor and the least common multiple of 48, 120, and 280. 

Solution. — 48 = 2^3 { q q j) _ o^ _ g 

120 = 2'.3.5 Hence, - ' ' ' 
280 = 215.7 ( I- C. M. ^- 2\3.5.7 = 1,680 



44 PEDAGOGICS OF ARITHMETIC. § 2 

Explanation. — The factor 2 is found 4 times in the first 
number, and only 3 times in each of the other two ; hence, 
2^ will exactly divide each of the numbers. The factor 3 
occurs in 48 and in 120, but not in 280. It is, therefore, not 
a factor of the greatest common divisor of all the numbers. 
The factors 5 and 7 are not found in all the numbers, and 
are hence not factors of the greatest common divisor. 

A number to be exactly divisible by 48 must contain the 
factors 2\'3; to be exactly divisible by 48 and 120, it must 
contain in combination both 2\3 and 2^3.5, or 2\3.o; and 
to be exactly divisible by 48, 120, and 280, it must contain 
in combination 2\3.5 and 215.7, or 2\3.5.7. 

38. Least Common Multiple by Division. — The 

following method is preferred by some teachers in cases 
where many numbers are involved : 

Example 1.— Find the L. C. M. of 36, 48, 60, 100, and 120. 
Solution.: — 2 

3 
2 
3 
5 

3, 2, 5 

Hence, L. C. M. = 2^3-.ry- = 3,600. 

Explanation. — The numbers are written in a row, as 
shown. Beginning with 2, the greatest prime number above 

1, we divide by it each of the numbers that will exactly 
contain it, and then divide each quotient in like manner by 

2, until no two C[Uotients will exactly contain 2. If at any 
time a number or one of the quotients will not exactly con- 
tain the divisor, that number or quotient is brought down 
into the quotient place. The next greater prime number 
that is contained exactly in two or more of the quotients is 
used as a divisor, and, as before, the division is continued 
until no two quotients will contain the divisor. Thus, the 
operation is continued until no two of the last row of quo- 
tients have a common prime factor. 

The continued product of all the divisors and the last 



3 6, 


4 8, 


6 0, 


1 0, 


1 20 


18, 


2 4, 


3 0, 


5 0, 


60 


9, 


1 3, 


15, 


2 5, 


30 


9, 


6, 


15, 


2 5, 


1 5 


3, 


3 


5, 


2 5, 


5 



2 



PEDAGOGlCvS OF ARITHMETIC. 



45 



quotients is the L. C. M. sought. This work may often be 
very much shortened by first canceling all numbers that will 
exactly divide any other number in the set. To illustrate, 
take the following example: 

ExA^n-i.E 3.— Find the L. C. M. of 18, 34, 30, 48, 73, and 130. 

Solution. — Since l8 is a divisor of 73, 34 of 48, and 30 of 130, these 
numbers may be omitted. The abbreviated method and that usually 
followed are both shown below. 

1 8, 2 4, 3 0, 4 8, 7 3, 1 3 



2 


4 8, 


7 3, 


120 


2 


24 


36 


60 


2 


1 2 


1 8 


3 


3 


6 


9 


1 5 



9 


1 3 


1 5 


34 


36 


60 


9 


6 


1 5 


1 2 


1 8 


30 


9 


3 


5 


6 


9 


1 5 


3 




5 


2 


3 


5 






5 


2 




5 



L. C. M = 2\3-.5 = 720. Ans. 



FRACTIOXS. 

39. Addition and Subtraction of Fractions by 
Inspection. — A very common occasion of error in adding 
and subtracting fractions is the want of fixed method and 
orderly arrangement. Where fractions may be readily added 
or subtracted by inspection, nothing should be written 
except the quantities and the result, but this should be done 
neatly and with an arrangement that every pupil knows to 
be obligatory. 

If mixed numbei-sare to be added, they should be written 
as shown on the left. The least common denominator is 
„ ^ recognized at once, and the addition should be 
9 I made without writing anything more than the 
4 I final result. Thus, in the first example, the 
1 1 tV pupils should be so familiar with the values of 
the fractions as expressed in 12ths that they 
can say very rapidly, "11, 21, 24, 30, 39, 47 



8f 
9f 

6 \ 

"I 
1 § 
1 2|v 
5 5 II 

Then. 



16| 

Hi 
64 3 



twelfths, equal to 3|.V; write \^ and carry 3." 
15, 25, 32, 3f^, 47, 55. Answer, 55|.V. " In the next 
example, also, pupils should be so well trained in 20ths that 



46 PEDAGOGICS OF ARITHMETIC. § 2 

they can go through the work without difficulty or hesita- 
tion. Thus, "12, 20, 34, 41), 5!», 75 twentieths, equal to 
3|, write f and carry 3." Then, "17, 33, 44, 48, 57, 64. 
Answer, 64 1. " 

"When fractions alone are to be added or subtracted, it is 
better to write them horizontally, separating them by plus 
or minus signs, and placing their sum or difference at the 
right after a sign of ecjuality. When the fractions are not 
beyond the limit fixed for inspection work, nothing should 
be written except the fractions and their sum or their differ- 
ence. Thus, 

1 _1_ 2 I 8. I il I li _ 6.ii — _7_ — qi • 4 _ 1 _ Ji_ . p4-p 
2l3T^9i<>T^18 — 18 — 2 — ^2' o 2 — 10' ^^'"• 

Of these the pupils should say only, "0, 21, 37, 52, 63 
eighteenths. Answer, 3V'; and " S, 3 tenths. Answer, j\." 

40. Written Forms in Addition and Subtraction 
of Fractions. — The teacher cannot be too exacting with 
reference to the forms that should be used in adding and 
subtracting fractions when written aid is necessary in the 
operation. These forms should be very definitely agreed 
upon and afterwards they should be followed in every detail, 
even the least. If this is not done, confusion and error are 
almost inevitable. Of course, the prime requisites in these 
forms are neatness and brevity. The following is the form 
preferred by the writer. 

Example 1. — Find the sum of |, |, ji, and ig. 

Solution. — 



2 


6, 8, 


1 8, 


30 


3 


3 4 


9 


1 5 




4 


3 


5 



C. M. = 2 X 3 X 4 X 3 X 5 = 360 
360 



6 

8 
18 
30 



60X5 = 


300 




4 5 X 7 = 


3 1 5 




2 0X11 = 


220 




12X19 = 


2 2 8 






1063 
360 ~ 


9 .•! 4 .3 



§2 



PEDAGUGICvS OP^ ARITHMETIC. 



4? 



Explanation. — First find the factors of the least common 
multiple of the denominators; indicate, and then find, this 
product. Divide this L. C. M. by each denominator in turn 
and multiply each result by the corresponding numerator. 
Find the sum of the products and divide it by the L. C. M. 
The quotient will be the sum of the fractions. Note that 
the reduction is made by the method of abbreviated division 
in which multiplication and subtraction are combined in one 
operation. This can always be done when the integral part 
of the quotient is not greater than l"^. 

ExAMi'i.K 2. — Find the sum of 5j\, ^Jf, 7||, and 8||. . 
Solution. — 7 11^, 2 !"> "> ■'>. 4 2 



L. C. M. = 6 X 7 X 5 
2 1 



310 



1 4 

2 1 

3 5 

42 



1 5 X 9 = 135 
1 X 13 = 13 

6X12= 72 

5 X 29 = 1 4 5 

48^^ 2 
2 10 

5+3+7+8=2 3 



Ans. 



The form for subtraction is precisely similar. 
ExAMi'LE o. — From ?,'^ take },l. 



L. C. M. = 2 X 3 X 9 X 16 = 576 



368 

1 53 

2 15 , 

■ . Ans. 

576 



Solution.— 


- 2 


3 6, 


64 




2 


1 8 


33 






9 


1 6 

5 7 6 






3 6 


1 6 






64 


9 



41, Special Cases in Addition and Subtraction of 
Fractions. — The sum of i- and ^ is equal to f. The numer- 
ator of this result is the sum, 2-}-'^) of the denominators and 



48 PEDAGOGICvS OF ARITHMETIC. § 2 

the denominator i.s the product, 2x3, of the same denomi- 
nators. Similarly, 

J :» + ! - 4X3 - '^ [ I "^ 5 - 5x3 - IT) I 

Inasmuch as it is frequently necessary to add or subtract 
two fractions having- 1 for numerators, children should 
be familiar with the following principles governing the 
operation : 

1. The sum of ti^'o fractions each Jiaving 1 for its uiiiner- 
ator is expressed by a fraction wJiose numerator is the sum, 
and its denominator t lie product, of their denominators. 

2. The difference between two fractions each Jiaving 1 for 
its denominator is expressed by a fraction zvhose numerator is 
the difference, and its denominator the product, of their 
denominators. 

It is clear that if the numerators of two fractions are each 
greater than 1, but alike, the same principles may be used 
in adding or snbtracting the fractions. 

Thus, since i + i = ^-^, or Vr, it follows that | + | 

_ '^(O + o) 1 fi . oonin 4 i 4 _ "*(' + ^) ^,. 4S Aico 3—1 

— g X 3 ' T5 ' agam, ^ -|- y _ ^^^ > "i 35- ^^ii^o, 4 5 



_ 3(5-4) _ _^_ 

~ 5X4 ~ 2«- 

This method is applicable only when the sum or the differ- 
ence of two fractions is to be found. If three or more such 
fractions are to be added, the usual method should be 
employed. 

It frequently happens that operations like the following 
are to be performed : 

This may be written as follows: 
f-1 + l-l + f+l-l + ^ + i = f + t+l + l + i + i-3. 

It is obvious that the value of the last expression may be 
found more easily than that of the first. Hence, where a 



§ 2 



PEDAGOGICS OF ARITHMETIC. 



49 



series of fractions requires both addition and subtraction, 
change each negative fraction into a positive fraction equal 
to the remainder obtained by subtracting the negative frac- 
tion from 1 ; then add all the positive fractions and from the 
result subtract 1 for each chantie that was made. 



ExAMi'LE 1. — Find the value of | — i -f- ^^Ij 



i + h 



Solution. — 


l + 3 + A + A + f + i- 


-3. 






2\4, 3, 14, 1 ( 


, 6, ^ 






7 b 


3 






L. C. D. =2X7 


X8X3 


= 336 






336 








4 


84X3 =-. 


252 






3 


1 1 2X2 = 


2 2 4 






14 


24X9 = 


2 1 6 






16 


21X9 = 


1 89 






(J 


56X5 = 


280 






8 


42X7 = 


294 








14 5 5 
3 36 


3 










1 JiJ^ 



Ans. 



Example 2.— Find the value of 5J - 2|' + 11 1', 
Solution.— J + | + ^^ + ^ + ^_3. 



6A-1! 



2 


>f, 


^, 1 5, 1 (), G 


3 


15 8 3 




5 8 


L. C. D. = 2 X 3 X ■') X 8 = 240 




24 


4 


60X3 = 180 


8 


3 0X3= 90 


1 5 


16X7 = 112 


1 


15X7= 105 


6 


4 0X1= 40 




52 7 




2 4 "'" 


G-1 + 


2^-^ 


7 _Q _ 1S47 _10 — A4 



Ans. 



42. Multii)lyini»- Mixed ^xiiubers. — In the multiplica- 
tion of one mixed number by another, it is almost universal 
usage to change both factors to improper fractions. It is, 



50 PEDAGOGICS OF ARITHMETIC. § 2 

however, much better to perform the operation in four 
steps. 

[ (1) t lie fraction by tJie fraction. 
I (2) tJie upper number by the lozvcr fraction. 
Multtply \ (3) tlie upper fraction by the knver number. 

(-4) the upper w!ioIe number by the hm'cr whole 
[^ number. 

The sum of these four results will be the correct product. 

E.XAMPLE 1.— Multiply 123 by llf ; also, 273.V by 48*. 
Solution.— 1 2 f 2 7 3 i 

llf 481 



i = (1) 1 X f 


§ = (1) |X| 


9 = (2) 13 X f 


2 1 8 g = (2) 273 X 1 


7 1 = (3) 11 X i 


2 4 = (3) 48 X 1 


132 = (4) 12X11 


13 10 4 = (4) 273 X 48 



1 4 8 f Ans. 1 3 3 4 6 i Ans. 

This method is peculiarly advantageous when the denomi- 
nators of the two fractions are equal. In this case, (2) and 
(3) above can be merged into one operation. 

Example 2.— Multiply 18f by 18J; also 15| by 121. 

Solution. — 

18| 15f 

18 4 12 4 



t\ = (1) fxf i = a)ixi 

27 = (2) + (3) 18X1 + 18X1 13 = (2) + (3) 15 X | + 12 X | 

324 == (4) 18 X 18 1 80 = (4) 12 X 15 

3 5 1 i\ Ans. 1 "3 3 I Ans. 

The student shottld notice that this method is only a 
special case of that in which numbers of two figures each are 
mtiltiplied together. The graphic symbols for the operation 
are | X I . 

In performing the part of the process denoted by the 
middle symbol X, the cross products may be united in one 
operation, if the fractions in the two factors have the same 
denominators. 

Thus, to mtiltiply 0| by Of the work represented by X may 
be done thus: 

times f + times | = 18 times |, or 12. 



§ 3 PEDAGOGICS OF ARITHMETIC. 51 

If the factors were 12f and 0^-, the work would be, 
12 times i + 9 times f = V'+V = ¥. ^v Of. 

A very compact method applicable where the terms of 
the fractions or the integral parts are large is the following: 

Example 3.— Multiply 28if by 19|. Also, 234§ by 98?. 

Solution.— 2 8 if 

195 



17 2 4 7 = 19 X 13 

8 I 140 = 28 X 5 

1 4 j\ = 247-^17 

1 7 t ' = 140 -H 8 

"^ ** ~ ISB 





234| 
98| 
4 9 = 
1 6 3 8 = 


98 X T) 
234 X 7 


2 


81f = 
182 = 
29 82 If 


490 ~ 
1638 -^ 9 





3 19 14 


Ans. 



564 jSj'^, Ans. 

Explanation. — First multiply the upper nmnerator 13 by 
the lower whole number li), getting 247. Before this, write 
the denominator IT as a divisor. Next multiply the lower 
numerator 5 by the upper integer 28, getting 140. Before 
140 write the denominator 8 as a divisor. Perform these 
divisions and write the results, 14Y"y and \7k, directly under- 
neath. Multiply 28 by 19 and write the result 532 as shown. 
Annex to 532 the product of \f by |. Add these numbers, 
and the sum will be the required product. 

The second example is solved in exactly the same manner. 

43. Canceling in Fractional Work. — Cancelation is 
one of the most useful expedients in arithmetic, and pupils 
should be taught to apply it whenever it can be done with 
a'dvantage. This is more frequently possible, perhaps, in 
multiplying and dividing fractions than anywhere else, and 
when these two operations are combined. The following 
operations will illustrate what is meant: 

Example 1.— Divide § X H X 7j\ by 4| X 81 X ff- 

Solution.- (§ X 5| X ^j\) - (4i X 8f X ||) = ^ ^ '^' ^ " 



8 X 29 X 84 X 5 X 7 X 33 

9 X 5 X 1 1 X 24 X 58 X 28 
V V' 1' 6 > V 



t* X ¥ X 
= ; = 11 Ans. 



52 PEDAGOGICS OF ARITHMETIC. § 2 

Explanation. — We first cancel 5 above and below. Then 
33 above and 9x11 below are canceled with 3 below as a 
quotient. This 3 with 28 below will cancel S-l above. 
Finally, 29 in 58 gives 2 below; this 2 in 8 gives 4 above, 
and 4 in 24 gives 6 below. 

Example 3.— Find the value of (§ X f ) -^ (| X W ' also, of (| of |f) -f- ■^\. 



1' >' 2 

(5 ctf 2i\ .^ 9 — 5 sy 2i \/ H — 2 AnS 

Y Y 3 

Example 3. — Find the value of 

11^ -(«^- 2^) -also, of 81X101X171 





V S V V V V 




69 51 53 5 6 10 


Solution. — 


"s^y^T-^ga-^ss-^so 




V V V 2 y '^' 



2|Xl|-H ' ' 18|Xl4iXB/j, 

Solution.— \ '%' . ' ^'' = -\°- X A X § X | X f X | = f = U- Ans. 

3X0 • 3 T T 1 1 ) 

Explanation. — f in the numerator is a divisor of -^^ and 
the result obtained is a divisor of *y^-. This requires what 
amounts to two inversions of f, which leaves it uninverted. 
The same is true of ^ in the denominator; it is a divisor of 
the entire numerator as well as of | of |. 



= I = 11. Ans. 



44. Cancelation Simplified. — If an error is suspected 
in canceling, it is usually impossible to verify the work 
without writing the entire solution a second time. This is 
owing to the fact that the numbers are usually crossed out 
and quotients written above and below until all legibility is 
destroyed. These causes of confusion may be avoided partly 
by using check marks instead of crossing out figures, and 
partly by writing no imnecessary quotients. This is illus- 
trated in the following examples showing the two methods: 

Example 1.— Divide 73 X 56 X 54 X 77 by 33 X 63 X 24 X 43. 
Solution. — 

V 8 V V ^ 8 ^ XX 

72 X 56 X 54 X 77 _ J^ x ^^ X ^^ X n _ . 

33 X 63 X 24 X 43 - °- ^''^- 33 X ^3 X ^^ X 4? ~ 



§ 2 PEDAGOGICS OF ARITHMETIC. 53 

Explanation. — The solution on the right illustrates the 
objectionable method usually employed, while that on the 
left shows the proposed improvement. Begin by consider- 
ing the numbers above and below very attentively. Time 
thus spent is not lost. 

We see that 24 below is contained in 72 above just 3 times. 
Check 24 and 72, but do not write the quotient 3 — carry it in 
your mind. Divide 33 by this quotient 3, placing a check 
mark under the former. By the quotient 11 divide 77 above, 
checking as before. The quotient above is now 7. Divide 
42 by 7, check 42 ; divide54by 6, and check; divide 63 by 9, and 
check; divide 56 by 7, and write the quotient 8. The check 
mark may be omitted where it is necessary to write a quotient. 

If it should be necessary to verify the work, everything 
except the original numbers may be easily erased. 

Example 2.— Find the value of 72x113X168x144x121 divided 
by 88 X 56 X 126 X 96 X 99. 
4 

3G V V V V 

„ 72X112X168X144X121 , . 

^°^""'°^"- 88X56X126X96X99 = ^- ^"^- 

V V y V V 

Explanation, — Check 56 and 112; quotient 2 above. 
Check 96; quotient 48 below. Check 144; quotient 3 above. 
Check 126; quotient 42 below. Check 168; quotient 4 
above. Check 88; quotient 22 below. Separate 22 into 
the factors 2 and 11 ; divide 72 by the 2 and write the 
quotient 36; with the factor 11 check 121; quotient 11 above. 
Check 99; quotient 9 below. Check 36; quotient 4 above. 
Write 4 as the answer. 

By proceeding with the factors somewhat differently, the 
entire solution may be finished without writing any quotient 
except the answer 4. 



V V 4 V V 

72 X 112 X 168 X 144 X 121 
88 X 56 X 126 X 96 X 99 

V V V V V 



= 4. Ans. 



Explanation.— 88x99 = 8x9x11x11. Check 88 and 
99. With 8X9 check 72; with 11x11 check 121. Check 
56 and 112; quotient 2 above. Check 96; quotient 48 below. 



54 PEDAGOGICS OF ARITHMETIC. § 2 

Check 144; quotient 3 above. Check 13(3; quotient 42 below. 
Check 168; quotient 4 above. Write 4 as the answer. 

If the teacher should wish to use such an example for class 
work on the blackboard, it would be necessary only to erase 
the check marks each time the exercise is assigned to another 
pupil. How the entire work may be done without writing 
any quotient but the final result may be held before the 
class as the perfection of operation to be sought. This can- 
not be done advantageously if the final result is a fraction or 
a mixed number; nor, indeed, is it desirable. Accuracy 
should not be sacrificed for performance. 

45. Inverting tlie Divisor in Division of Frac- 
tions. — As long as teachers are examined, one of the stand- 
ard questions that they will be required to answer will be, 
" In division of fractions why do you invert the divisor and 
multiply ? " It is not enough to say that multiplying by the 
reciprocal of a number is the same as dividing by the num- 
ber itself. It is one of those questions of which the difficulty 
lies in the fact that the matter is so simple. Proving the 
correctness of the rule for division of fractions is very much 
like proving an axiom. Perhaps there is no way more easy 
to be understood than the following method by induction: 

Since 8 dollars divided by 2 dollars gives a quotient of f , 
or 4 ; and, since 8 days divided by 2 days gives also a quo- 
tient of f , or 4, we may conclude that 8 things of any kind 
divided by 2 things of the same kind will give the same 
quotient 4. Hence, 8 thirds divided by 2 thirds^ or •|-^-|, 
equals 4; also-V«--^f = 10-^3 = Jt^. Further, 



10- 


^3 


10 

— 3 • 




9_ _- 


8- 


-9 = f 


; 





12- 


-10 = 


1 2 
TO 


5 -— 


J-"- - 


.15 — 
• "If" — 


10 



■|2_^01 — 5_^.5 — in_:_15 — lO-^lfi — 10 
I3 . ^., — 3 . 2 — -g- . -5- — IW . 1,J _ j^. 

Now in each of these divisions the result would have been 
the same if the divisor had been inverted and the operation 
changed to multiplication. (It must be remembered, how- 
ever, that any integral quantity may be written as a fraction 

*o 2 

whose denominator is 1. Thus, $5 = -— , 2 = -, etc.) 



§ 2 PEDAGOGICvS OF ARITHMETIC. 55 

Taking- in order the foregoing examples, 

, , „ 8 dollars 8 dollars 1 8 

8 dollars -f- 2 dollars = = -r X^i,, =5 = 4; 

2 dollars 1 2 dollars 2 

8 days 8 days 1 8 

8 days -^ 2 days = irzr^ =T X^i i =o = 4; 

2 days 1 2 days 2 

V 
U O W •-* Q 

8 thirds -r- 2 thirds = '.^ -- ^ = - X [^ = :i = 4 ; 

V 

,„ , 10 7 10 2 3 2 4 8 

10_!_3 — V- — • : — — V— — • 

■r ■ T - q ^3- s' 'S- 4 3^3~9' 

. , 4 3 12 ,,' .^, 5 5 5 2 10 

5 -3-5^2" 10" ' ' -~3'2 3^5 ~ 15' 
Since, when the denominators are the same, we divide the 
numerator of the dividend by the numerator of the divisor in 
order to divide the dividend by the divisor; and, since the 
same result is obtained by inverting the terms of the divisor 
and multiplying, we infer the following by induction : 

Rule. — Invert the tci'ins of the divisor and proceed as in 
inultiplieatioji. 

46. Greatest Coninion Divisor of Fractions. — In 

studying the subjects of the Greatest Common Divisor and 
the Least Common Multiple of whole numbers, pupils are 
very likely to inquire about the method to be pursued in the 
case of fractions and mixed numbers. For the teacher to be 
unable to answer such inquiries satisfactorily is not only 
embarassing, but it loses him a certain prestige of the highest 
value. Moreover, there are frequent occasions in practice 
when the process must be applied. For these reasons the 
subjects will be explained. It is first important to indicate 
exactly what is intended by the expression at the head of 
this article. This may best be done by recalling the matter 
with respect to integers. 

Definition. — T/ie greatest conn/ion divisor (G. C. D.) of 
two or more whole numbers is the greatest wJiole number that 
will divide each of the numbers and give an integral quotient. 

Thus, since 12 is the greatest whole number that will 
exactly divide 36, GO, and OG, it is the greatest common 
divisor (G. C. D.) of 36, 60, and 96. 



56 PEDAGOGICS OF ARITHMETIC. § 2 

Definition. — The greatest conivion divisor [G. C. D.) of 
tivo or more fractional numbers is the greatest fraetional 
mimber that ivill divide each of the numbers and give an 
integral qnotioit. 

Thus, the G. C. D. of 2%, \\, and f f is ■^-^, since if these 
fractions be in turn divided by /g-, the respective quotients 
are the whole numbers 2, 3, and 7. If -^^ were not the 
G. C. D., 2,' 3, and 7 would have a common integral factor 
greater than 1. 

It is evident from the foregoing that when several fractions 
have the same denominator, their G. C. D. is a fraction having 
the same denominator as the fractions, and a numerator 
equal to the G. C. D. of the numerators of the fractions. 
This may be more fully shown by solving some examples. 

Example 1. — Find the greatest common divisor of |, |, and y'j. 

^ 3 3, 12 15 18 ^ ,^ ^ ,12,15,18 „ . 
Solution.— |, |, ^^ = _, — , _. G. C. D. of ^ = 2%- Ans. 

Explanation. — The fractions are first changed to equiva- 
lent fractions having the L. C. D. Then it is evident 
that the G. C. D. of if, \%, and \\ is also the G. C. D. 
of f , |, and -^-^. But we know by inspection that the G. C. D. 
of 12, 15, and 18 twentieths is 3 twentieths. 

Example 2.— Find the G. C. D. of 6f, 4|, 4i, and 6|. 

Solution.— 6|, 4i, 4i 6| = ^j^, %, ~, ~. 

4' _ 5 5 4 2 5 5 

G. C. D. of 27, 9, 21, 33 _ ^ . 
L. C. M. of 4, 2, 5, 5 ~ 20' "^" 

Explanation. — Reduce the numbers to improper fractions. 
Find the G. C. D. of the numerators, and write the result over 
the L. C. M. of the denominators. 

To show that there will be an integral quotient when each 
of the numbers is divided by the G. C. D. , the division may 
be performed : 

6f^^ = 5xf = 45;4i-^^ = |xf = 30; 
^6 • 2W - 5 X 3 - -», O5 . ,^ - g X 3 - 44. 



§ 2 PEDAGOGICS OF ARITHMETIC. 57 

Now, since these quotients, 45, 30, 28, and 44, have no other 
integral common divisor greater than 1, it follows that y\ is 
the (CJ'catcst common divisor of the given numbers. 



EXAMPLES FOR PRACTICE. 
4: < . Find the greatest common divisor of the following: 



[a) 


s 


5 

5' 


2 
3- 


{e) 


51- 


4? 

^8' 


16|. 




r(«) 


1 

T2- 


(^) 


(^) 


4 
5- 


|. 


8 
T5- 


(/) 


5 * 


101, 


12^. 


Ans. - 


(^) 


A- 


(/) 


ic) 


5 
6' 


5 

5' 


1 

27- 


U) 


7i 


4f, 


m- 




(0 


5 
51- 


U) 


{d) 


3 


6 

7' 


15 

2 8- 


(/o 


3|. 


si, 


A\. 




U^o 


3 

2 8- 


(/') 



48. Least Common Multiple of Fractions. — Very 
similar to the process of finding the greatest common divisor 
of fractions is that of finding their least common multiple. 

Definition. — The least comuion multiple {L. C. M.) of two 
or more fraetional Jiumbers is the least fiuviber, integral or 
fractional, that z^'ill contain each of them a zvhole nninber of 
times. 

Example 1. — Find the least common multiple of |, |, |, and |. 



Solution. — 



5 — 2? ' ? — 2? ' g ~ 2? ' 8 — 2^ 

L. C. M. of 16, 18, 20, 15 = 720. 



^ ^ ^^ ^ 16 18 20 15 720 ^^ , 
L. C. M. of ^^, _, ^, _ = _ = 30. Ans. 

Explanation, — Reducing the fractions to equivalent 
fractions having the L. C. D. , we have IG, 18, 20, and 15 
twenty-fourths. Now it is evident that the L. C. M. is a 
number of twenty-fourths equal to the L. C. M. of the 
numerators. 

This same result may be obtained by writing the fractions 
in their simplest forms, and then dividing the L. C. M. of the 
numerators by the G. C. D. of the denominators. 

^, L. C. M. of 2, 3, 5, 5 30 „,, . 

^^"^- G.C.D.of3.4,6.8 = T=^'^- ^"^- 

The former method is to be preferred, for if any of the 
fractions is not in its simplest form, the result, although 
it is a common multiple, is not the least common multiple. 



58 PEDAGOGICS OF ARITHMETIC. § 2 

Suppose, for example, f be written as y\, and the other frac- 
tions be in simplest form. 

L. C. M. of 8. 3, 5. 5 _ 120 _ 
G. C. D. of 12, 4, 6, 8 ~ 2 ~ ' 

Again, let both | and | be written as twelfths. 

L. C. M. of 8. 9. 5, 5 _ 360 _ 
G. C. D. of 12, 12, 6, 8 ~ ^ ~ 

Example 2. — Find the least common multiple of li, 2g, and 2|. 
Solution.— l?, = |; 2| = V; 2| = V- 

AT „C /I 10 ie ,tU 

48. Ans. 



L. 


C. 


M. 


of 4, 


12, 


16 


48 


G. 


C. 


D. 


of 3, 


5, 


7 


1 



EXAMPLES lOU PRACTICE. 

49. Find the least common multiple of the following: 



(a) 


g- 


15 • 


('-) 


2 3 8 
3' 3' 9- 




{t>) 


8 
5' 


3 


(7) 


.5 7 14 
g- T3' 15- 


A 


(0 


4',, 


n- 


(M) 


03 Q5 71 

-J. Og, (j. 


(^0 


or, 

~8' 


H- 


(/o 


11 2 fJ2 
't' ■^i' "S- 







' ('0 


311. 


(^■) 


24. 


ns. "1 

1 


(0 


24. 

18. 


(/') 
(A-) 


231. 
79|. 


1 


L('0 


147. 


(/O 


120. 



DENC)>riX.\TE NUMHERS. 

50. ISIattc^rs Important and Unimportant in Denom- 
inate Xnmbers. — Perhaps more time is wasted in the study 
of unimportant matters in denominate numbers than in any 
other arithmetical subject. Some of these are English money, 
and addition, multiplication, and division of compound num- 
bers. In business operations, the only use for subtraction 
of compound numbers is in finding- the difference between 
dates, but the more exact method now employed by business 
men obviates the necessity for the plan of twenty years ago. 
About the only other use for subtraction of compound num- 
bers is in finding the difference between two angles, in 
trig'onometrical calculations. 

For retaining English money in our arithmetics, there is 
no reason that is not equally good for German, French, or 
Spanish money. When this country was merely a colony of 
England and the coinage of the mother country was in use 



§ 2 PEDAGOGICS OF ARITHMETIC. 59 

here, our boys and girls had to be taught to count it ; but 
when we adopted the decimal system and discarded the 
coinage of England, the subject might have been omitted 
from our textbooks. Unless one visits Europe, he never 
has the slightest need to know about pounds, shillings, and 
pence, and even that event furnishes an equally good 
argument for studying the coinage of European countries 
other than England. The retention of the subject in our 
books illustrates how conservative we are, notwithstanding 
our boasted progress. For many years the coinage of Spain 
was in use here, but we never introduced it into our school 
books. 

It is difficult to imagine a situation in actual business in 
which it would be necessary to add, multiply, or divide denom- 
inate numbers. The same may be said of reduction a,scend- 
ing, so called, and reduction descending. The important 
thing is to have the pupil perfectly familiar with the useful 
tables. In learning them, he should, as far as is possible, see 
and handle the weights and measures actually used in busi- 
ness. The measures of length, surface, and volume he can 
easily and profitably make for himself. The dimensions of 
the class room, the areas of floors, walls, and ceilings, and the 
volumes of various rectangular spaces may be found by the 
pupils themselves, and thus they will become familiar with 
the most important units of mea.surement. The measures 
of capacity can be procured without much expense, and after 
they have been obtained they should last indefinitely. 

51. Order. — If any particular order is preferable in pre- 
senting the tables of denominate numbers, it is perhaps the 
following : 



1. 


Measures of Length. 






2 


Measures of Surface. 










(^? 


Space. 


3. 


Measures of Volume. 


1 


Wood. 
Stone. 


4. 


Measures of Capacity. 


W^ 

'l^> 


Liquid. 
Dry. 



60 PEDAGOGICS OF ARITHMETIC. S 2 



5. 


Measures of Weight. 


'a 
- b 


Avoirdupois. 
Troy. 


6. 


Time. 


1 


Apothecaries 


7. 
8. 


Counting. 
Stationery. 







{a Lumber. 

b Plastering. 

9. Practical Measurements. { c Painting-. 

d Shingling. 

c Lathing, etc. 

If reduction involving decimals were excluded from our 
courses of study, there would be undoubted gain. Nobody 
has ever been required by the exigencies of business to 
change .87 of a year to units of lower denomination, or to 
reduce 17 days 5 hours 31 minutes and 19 seconds to the 
decimal of a year. There are so many things having a 
direct and important bearing upon the concerns of life, 
that it seems a pity to fritter away valuable time with 
matters of no consequence. 

53. Classiflcatioii of tlie Processes of Denominate 
Numbers. — All the operations in denominate numbers may 
be referred to two main classes. These are : 

1. Reduction. — Of reduction there are two kinds, {a) 
reduction descending, and (/;") reduction ascending. 

2. Fundamental Operations. — The fundamental opera- 
tions with denominate numbers include {a) addition, {b) 
subtraction, {c) multiplication, and {d^ division. All these 
processes are important, and should be thoroughly taught. 
Especially important is it that the pupil should know the 
best and briefest methods, and an arrangement of work least 
likely to lead to error and confusion; for with units of meas- 
ure that change with each advance from lower to higher, 
denominate numbers will always be to most pupils a trouble- 
some subject. On account of this fact, examples with their 
solution, illustrating every operation likely to be met in 
denominate numbers will now be given. 



§ 2 PEDAGOGICS OF ARITHMETIC. 61 

53. Keduetioii Descending;. — Before entering upon 
the solution of examples, the student should carefully note 
the following definitions: 

Definition. — The reduction of a denominate number is 
the process of changing its denomination without altering its 
value. 

Thus, changing miles to feet, or quarts to bushels is reduc- 
tion. 

Definition. — Reduction desceruling is the process of chang- 
ing a denoini)iate number to an equivalent denominate nundn-r 
of lower denomifiation. 

Thus, changing miles to inches, or years to hours or 
minutes is reduction descending. 

Definition. — Reduction ascending is the process of chang- 
ing a denominate number to an equivalent denominate number 
of higher denomination. 

Thus, changing pounds to tons, or square feet to acres or 
square miles is reduction ascending. 

There are two cases of reduction descending: 

1. To reduce a compound denominate number to lower 
denominations. 

Example 1. — Change 3 mi. 189 rd. 5 yd. 2 ft. to inches. 
Solution.— 3 mi. 189 rd. 5 yd. 2 ft. 

320 



1149 

5 1 


rd. 


5 74 1 
5750 " 




6 3 2 4 1 
3" 


yd. 


18975 1 
1 2 


ft. 



2 2 7 7 6 in. Ans. 
Explanation. — Change 3 miles 189 rods to rods by mul- 
tiplying the number of miles by 330 and adding 189 to the 
product. This should be done in one operation. Change 
1,149 rods 5 yards to yards by multiplying the number of 



62 PEDAGOGICS OF ARITHMETIC. § 3 

rods by 5^ and adding 5 to the product. In doing this mul- 
tiply first by ^. Change (:;,32-4^ yards 2 feet to feet by multi- 
plying the number of yards by 3 and adding 2 to the product. 
Change the feet to inches by multiplying the number of feet 
by 12. 

2. To reduce a doiomiiiate fraction to integers of loiver 
denouiinatioii. 

There are two slightly different varieties of this case: 
[a) when the fraction is a common fraction; (/;) when the 
fraction is a decimal. These cases are both exemplified 
below. 

Example 2. — Reduce f of a mile to integers of lower denomination. 

Soi-UTioN. — 5 mi. 

320 



6)1600(266 rd. 
4 



6)22 ( 3 yd. 
4 
3 



6 ) 1 2 ( 2 ft. 

Explanation. — f «£ 1 ""^ilc is i of 5 miles. Change 

5 miles to rods and divide by (i. Change the remaining 

4 rods to yards and divide by 0. Change the remaining 

4 yards to feet and divide by 6. In dividing write only 
quotients and remainders. 

E.XAMPLE 3.— Reduce .90625 of a gallon to integers of lower denomi- 
nation. 

Solution.— .906 2 5 gal. 

4 
3.62500 qt. 

2 

1.2 5 pt. 
4 



1.0 gi. 
3 qt. 1 pt. 1 gi. Ans. 

Explanation. — Since a part of a gallon expressed dec- 
imally is reduced to quarts in exactly the same way as a 
whole number of gallons, we multiply by 4, and point off 



2 



PEDAGOGICS OF ARITHMETIC. 



63 



5 places in the product. Next, reduce .025 quarts to pints, 
and finally, .'25 pints to gills. Note that the part of the 
product falling to the left of the decimal is not multiplied. 



54. Reduction Ascending. — There are two well defined 
cases of reduction ascending, and a third case that may 
properly be referred to this division. 

1. To reduce a deiiouiiiiate number to higJier de)iouii)ia- 
tions. 

Example 1. — Change 98,329 inches to higher denominations. 



Solution. 



12 
3 
5 



1 1 
320 



3 2 9 in. 



1 !t 4 ft. 1 in. 



2 7 8 1 vd. 1 ft. 



5 4 6 2 half -yd. 



4 9 6 rd., (j half-yd. = 8 yd. 



1 mi. 176 rd. 

1 mi. 176 rd. 3 yd. 1 ft. 1 in. Ans. 

2. To reduce a denominate fraction, common or decimal, 
to an equivalent fraction of higher denomination. 

Example 2. — Change 4^ feet to the fraction of a mile. Also .75 of a 
pint to the decimal of a gallon. 



Solution.— ^ -^ 16| -f- 320 = f X u's X sh = 



Ans. 



Explanation. — Dividing the feet by 10^ changes to rods, 
and dividing that result by 320 changes to miles, as required. 
The steps in the process are obvious. 



Solution.^ 



.7 5 pt. 



.3 7 5 qt. 



.09375 gal. Ans. 



Explanation. — The process and the reasons for it are 
exactly the same as with integers, except that care is required 
with reference to the decimal point. Note that the second 
point stands directly under the first, and the third tmder the 
second. 

3. To reduce a compound denouiinate number to a fraction 
of some other compound denominate )t umber of greater value. 



64 PEDAGOGICS OF ARITHMETIC. § 2 

Example 3. — What common and what decimal fraction denotes the 
part that 1 bu. 1 pk. 3 qt. 1 pt. is of 2 bu. ? 

Solution.— 1 bu. 1 pk. 3 qt. 1 pt. _ 87 pt. 87 



2 bu. 128 pt. 128 

-V- 128 - .6796875. Ans. 



Ans. 



55, Addition of Coiiii)oiiiid Deiioininate Numbers. 

The student can have no difficulty with the addition of com- 
pound denominate numbers, unless it be in examples like 
the following: 

Example 1. — Find the sum of 59 mi. 95 rd. 4 yd. 2 ft. 9 in., 97 mi. 
200 rd. 3 yd. 1 ft. 8 in., 75 mi. 171 rd. 2 ft. 5 in. 
Solution. — 



niL 
5 9 


rd. 
9 5 


yd. 
4 


ft. 

2 


in. 
9 


97 


200 


3 


1 


8 


7 5 


1 71 





2 


5 


232 


147 


3 1 





1 






1 - 


= 1 


6 



23 2 147 3 2 4 

Explanation. — The first column = 22 inches, or 1 foot 
10 inches. Write 10 inches and carry 1 foot to the next 
column. The second column = 2 yards feet. Write feet 
and carry 2 yards to the next column. The column of 
yards = 9 yards, or 1 rod 3|- yards. Write 3^ yards and 
carry 1 rod to the next column. The next column = 467 rods, 
or 1 mile 147 rods. Write 147 rods and carry 1 mile to the next 
column. The last column = 232 miles, which is to be written 
under the last column. Finally, ^ yard = 1 foot 6 inches, 
which must be written under the proper columns and added. 

56. Subtraction of Componnd Denominate Num- 
bers. — The chief interest and use of subtraction of denomi- 
nate numbers is in finding- the difference between dates. 
The following method, which counts 12 months of 30 days 
each as making a year, was exclusively used: 

Example 2. — A certain man was born February 12, 1822, and died 
January 5, 1890. How long did he live ? 

Solution. — yr. mo. da. 

1890 1 5 

18 2 2 2 12 

67 10 23 



§ 2 PEDAGOGICS OF ARITHMETIC. 65 

Explanation. — The second column shows the ntimber or 
place of the months mentioned. Thus, January is the first 
month, February is the second month, and so on. Since 
12 days cannot be taken from 5 days, it is necessary to bor- 
row 1 month, 30 days, from the column of months. This 
is added to the 5 days and 12 days subtracted from the sum, 
leaving 23 days. The month borrowed reduced the 1 month 
in the minuend to 0. vSince 2 months cannot be taken 
from months, we borrow 1 year from 1890 years, leaving- 
1889 years. Subtracting, now, the 2 months from 1 year, 
or 12 months, we have 10 months. Finally, we subtract 
1822 years from 1889 years, and write the remainder, 07 years, 
as the last item of the answer. 

There are three methods of finding the difference between 
two dates. One of these is the method shown above. The 
other two have come into u-se in calculating exact interest, 
which is now employed by the United States Government 
and by most banks. This method assumes that there are 
365 or 366 days in a year and not 360 days. It is gaining 
rapidly in favor among business men, and will doubtless be 
adopted imiversally. To show the three methods together 
we shall now give the solution of the same example by each 
method. 

Example 3. — Find the time from January 29, 1883, to August 15, 1884. 

Solution. — {a) First method. 

yr. mo. da. 

1884 8 15 

1882 1 29 

3 6 16 

Explanation. — The years, months, and days are written 
and subtracted as already explained, giving 2 years, 6 months, 
and 16 days. 

{b) Second method. 

Jan. 29, 1883, to Jan. 29, 1884 = 2 yr. \ 
Jan. 29, 1884, to July 39, 1884 = 6 mo. [ Ans. 
July 29, 1884, to Aug. 15, 1884 = 17 da. ) 

Explanation. — The number of whole years is first found 
— 2 years. Next, the number of whole months included 



6G PEDAGOGICvS OF ARITHMETIC. § 2 

between January 29, 1884, and August 15, 1884. This is 
6 months. Finally, the days from the end of the 6 whole 
months to the end of the time, August 15, or 17 days. 
This is 1 day more than the result obtained by the first 
method. 

(t) Third tnef/iod. 

Jan. 29, 1882, to Jan. 29, 1884 = 2 yr. 

Jan. F'eb. Mar. Apr. May June July Aug. 

2 + 29 + 31 + 30 + 31 + 30 + 31 + 15 = 199 da. 

Explanation. — The number of whole years is first foimd, 
and then the number of days. In estimating exact interest 
the third method is usually employed. By this method, 
2 years 199 days is regarded as 2^ff years. When, however, 
the period ends within a leap year, and after February 28, 
the denominator of the fraction is IJGG. In the case of the 
foregoing example, since the time ends in August, 1884, a 
leap year, the result is regarded for the .second method as 
2^ years + -^^ years. By the third method it is 2^f 
years. 

The following example illustrates a method of solution 
in which it is sometimes necessary to borrow more than one 
unit from the next higher denomination : 

Example 4. — After traveling 20 mi. 400 rd. 10 yd. IT ft. 20 in., how 
much farther will make a distance of 30 miles ? 
Solution. — mi. rd. yd. ft. in. 

3 

20 400 10 17 2 

~8 2^6 5 2 4 

Explanation. — First borrow 2 feet, or 24 inches. Then 
borrow 7 yards, or 21 feet, and subtract 17 feet + 2 feet 
borrowed. Next, borrow 4 rods, or 22 yards, and subtract 
10 yards + 7 yards borrowed. Borrow 2 miles, or 640 rods, 
and subtract 400 rods + 4 rods borrowed. Finally, subtract 
20 miles + 2 miles borrowed. 

The example might have been solved by reducing the 
subtrahend to 21 mi. 82 rd. 5 yd. ft. 8 in., and then subtract- 
ing in the usual way. Or, the minuend might have been 
written as 28 mi. 636 rd. 15 yd. 19 ft. 24 in. 



§ 2 PEDAGOGICvS OF ARITHMETIC. 07 

57. Multiplication of Denominate Xunibers. — 

Ordinary multiplication of denominate numbers involves 
no principle of reduction not included in addition of denom- 
inate numbers; for, as is well known, multiplication is in 
reality only the process of adding two or more equal nimi- 
bers. Formerly, however, there was a process employed 
by artificers in finding areas and volumes when dimensions 
were given in feet and duodecimal divisions of a foot. This 
process was called duodecimals, but it is no longer used to 
any extent. 

The notation of duodecimals was formerly somewhat dif- 
ferent from what it is now. The table as found in the old 
works on mensuration reads as follows: 

12 fourths ("") = 1 third, written 1'", 

12 thirds = 1 second, " 1", 

12 seconds = 1 inch, or prime, " 1 in. or 1', 

12 inches = 1 foot. " 1 ft. 

The only duodecimal divisions now in general use are the 
foot and iiicJi ; the abbreviations for these are ft. or ', and 
in. or ". Thus, the dimensions of a joist 20 feet long, 6 inches 
wide, and 4 inches thick may be written 20'x'Vx4''. 

In order to show the operation of multiplying duodecimals, 
the following example will be solved by the method formerly 
employed and by that used at present. 

Example. — Find the area of a floor 20 ft. 7 in. long and 16 ft. Sin. wide. 
Solution. — 

Explanation. — Beginning at the right, 
8'x7' = 5()" = 4' 8". This means that 
56 square inches = 4 strips each 12 inches 
long and 1 inch wide, and 8 square inches 
besides. We write 8" and carry the 4'. 
20 ft. X 8' = 1(30' (strips 12 inches long and 1 inch wide) 
= 13 square feet 8'. Next we multiply by 10; 10 ft. x7' 
= 112' = square feet 4'. We write 4' and carry 9 square 
feet. .sq. ft. + 20 ft. x 10 ft. = 329 square feet. The addition 
of the partial products is obvious. 

In this result, 8" = |^, or | = ^ .sq. ft. = ^ sq. ft. 



2 ft. 
1 6 ft. 




7' 
8' 




1 3 sq. 
32 9 •' 


ft. 


8' 
4' 


8" 


3 4 3 sq. 


ft. 


0' 


8" 



G8 



PEDAGOGICvS OF ARITHMETIC. 



§2 



Hence, the answer is the same as would be obtained by the 

ordinary process. Thus, 

(20 ft. 7 in.) X (16 ft. 8 in.) = 20yV ft. X 16| ft. = 343yV sq. ft. 

The teacher will remember that, strictly speaking, feet 
cannot be multiplied by feet or inches by inches. The 
multiplier is always abstract and the product is of the 
same denomination as the multiplicand. In finding- areas and 
volumes we are told to multiply together certain dimensions 

}. * ittr. H expressed in linear units, 

such as yards, feet, inches, 



Area of rectanfile=4 



1 sq. i/n. 



sq.m.x.3=12 sq.in. 



1 sq. in. 



1 sq.i'H. 



1 sq.in. 



Fig. 



meters, etc. But we do 
not, in reality, perform any 
such multiplication. This 
fact will be apparent from 
the diagram. Fig. 7. This 
represents a rectangle 
4"x3". By drawing lines, 
this rectangle may be divi- 
ded into three rows each 
containing 4 square inches. Since one row contains 4 square 
inches, 3 rows will contain 3 times 4 square inches. When 
areas, then, seem to be found by multiplying inches by inches, 
feet by feet, etc., nothing of the kind happens. A similar 
explanation of the rule for volumes may be made and illus- 
trated by a drawing. 

58. Division of Denominate !N"unibei's. — There are 
two general cases of division of denominate numbers. 

1. To divide a compound denominate number by an abstract 
number. 

Example 1.— Divide 17 mi. 189 rd. 4 yd. 3 ft. 9 in. by 13. 

Solution. — 



mi, 
13)17 



rd. 
1 89 



yd. 
4 



Explanation. — 17 miles 
divided by 12 gives 1 mile with 
5 miles remaining. 5 miles -j- 189 
rods = 1,789 rods. This divided 
by 12 gives 149 rods with 1 rod remaining. 1 rod + 4 yards 
= 9|- yards. 9|- yards divided by 12 gives yards with a 



149 8 7i 



§ 2 PEDAGOGICS OF ARITHMETIC. 69 

remainder of 9.V yards. The sum of 9i yards and 2 feet 
= 30|- feet. This divided by 12 gives 2 feet with a remain- 
der of G|- feet. The sum of 6^ feet and inches = 87 inches. 
Dividing 87 inches by 12 gives a quotient of 7^ inches. 

2. 7^0 divide one compound denominate ninnber by another 
of the same e/ass. 

Example 2. — In how many weeks at 18s. lid. per week can a person 

earn £25 10s. 9d. ? 

£25 10s. 9d. 6129d. ^^ . 

Solution.— — r^ — jj^ = - ...r.^ - ==2/. Ans. 

18s. lid. 227d. 

Explanation, — The dividend and divisor are both reduced 
to the same denomination, and the quotient is then found in 
the ordinary way. 

Under this case may be included the division of a denomi- 
nate fraction, common or decimal, by another denominate 
fraction of the same class. This is substantially the second 
case under reduction ascending, which has already been 
exemplified and explained. 

59. Abbreviations iii Denominate Numbers. — There 
is, perhaps, no question relating to the exact sciences that is 
more unsettled than that concerning the form in which 
abbreviations for the various denominate numbers should 
be written. This is shown more in the plural than in the 
singular forms. A few illustrations will make the matter 
apparent. 

The Standard Dictionary gives the following singular and 
plural forms for barrel : singular, brl. , bl., bar., bbl. ; 
plural, brls., bis., bbls. Now it is evident that there is 
no real need for more than two of these seven forms; it is 
not, however, clear which two are best. The dictionary is 
supposed to reveal current authorized usage, and, doubtless, 
it does so; but it is unfortunate that there are so many ways 
of denoting the same thing when the result is only con- 
fusion and uncertainty. 

Every teacher should have a well considered scheme of 
abbreviations from which he never varies. The Inter- 
national Correspondence Schools have adopted the rule that 



70 PEDAGOGICS OF ARITHMETIC. § 2 

"all abbreviations of the names of denominate ninnbers are 
to be printed in the sing-ular form." The reason for this is 
that the sing-ular form is usually the simplest, and, if intelli- 
gible and in general use, the simplest form is always the best. 
The only dii^iculty arising in the application of this rule is 
in cases where there are two or more singular abbreviations 
for the same word. Thus, the word barrel is variously 
abbreviated in the singular by bar.^ bl., brl., and bbl. In 
such cases, the student should prefer the simplest form 
unless there is another having more general currency. Of 
the four abbreviations given above there is no doubt that 
bbl. should have the preference. 

60. Abbreviations in tbe Metric System. — The sys- 
tem of abbreviations used for the metric system is a good 
one; indeed, it would not be easy to imagine how it could 
be improved. It is very simple and imambiguous. For 
linear measures, including the millimeter, centimeter, deci- 
meter, meter, decameter, hectometer, kilometer, and myria- 
meter, the respective abbreviations are mm., cm., dm., m,, 
Dm., Hm., Km., and Mm. The abbreviations for square 
and for ciibic measure are the same, with exponents. Thus, 
mm"., m^, Hm". , etc., and cm\, ml (stere) denote respect- 
ively square millimeter, square meter, square hectometer, 
or hectare, cubic centimeter, and cubic meter. 

For the measures of weight and capacity, we have the 
principal units, the gram (g.) and the liter (1.), besides the 
following : 

Milli 

Centi 

Deci 

Deca 

Hecto 

Kilo 

Myria 

The student will note that measures greater than the 
principal unit in each table begin their abbreviations with 
capitals and all the others begin with small letters. It will 



gram: mg., eg., dg., g., Dg., Hg., Kg., Mg. 
liter: ml., cl., dh, 1., Dl., HI., Kl., Ml. 



§ 2 PEDAGOGICS OF ARITHMETIC. 71 

be observed, too, that the names of the measures below and 
including the principal unit are formed with Latin prefixes, 
while those that are greater than the pi'lncipal unit have 
Greek prefixes. The former are inilli, ccnti, and dcci ; the 
latter are dixa {StKa, deka), hecto {eKarov, hekaton), /:i7o 
{jiXioi, chilioi), viyria (iivpioi, myrioi). 



PERCENTAGE. 

61. Importance of Percentage. — There is no subject 
in the whole compass of arithmetic of so much practical 
value as that of percentage. Its application to every variety 
of business in which men are engaged renders it imperative 
that whatever matter is neglected in the education of our 
children, this must not be one of them. If percentage' be 
well mastered, it is almost a foregone conclusion that the 
other subjects will be. The decimal system, which is the 
basis of percentage, has no more convincing illustration of 
its value than we find here. Our advice to the teacher would 
be to review the subject until the pupil is familiar with every 
phase and modification of it. While a certain incurable con- 
servatism prevents us from availing ourselves of the incal- 
culable advantage of a general application of the decimal 
systein to the concerns of life, we should utilize it in the 
fullest measure in which it has been accepted. 

62. Three Methods in Percentage. — There are three 
quite distinct methods of solving examples in percentage : 
(1) the decimal method; (3) the method by covimon frac- 
tions^ or analysis; (o) the method hy formulas. Each of 
these methods has its advocates among teachers, and there 
is little probability that the question of superiority will ever 
be settled. It is highly probable that they are of nearly 
equal general importance, while for each particular problem 
to be solved, one of the three plans is specially suited, and is 
therefore better for that problem than either of the other 
two. If this view be correct, then it is clear that all three 
should be carefully taught, and that the pupil's mastery of 



72 PEDAGOGICS OF ARITHMETIC. § 2 

each should be so full that he can judge correctly which 
method is best for each particular problem. There are so 
many applications of percentage both with and without the 
element of time that there is abundant opportunity to learn 
all three of the methods. These three methods will now be 
explained and exemplified. 

63. The Decimal Method of Percentage. — Since the 
word percentage is derived from the two Latin words, per, 
" by " or " on, " and ccntiun, ' ' a hundred, " its meaning makes 
clear that the subject relates to decimal {licccm, "ten") 
matters. Twenty-five per centiun means no more than 25 
on 100, and this expressed in the ordinary decimal notation 
is .25. vSo that to find any per cent, of a number is merely 
a case of multiplication of decimals — usually the finding of 
so many hundredths. A few examples will serve to show 
exactly what is meant by the decimal method of percentage. 

Example 1. — A man bought a house for §8,675 and sold it at a gain 
of 35^. What did he gain by the transaction ? 
Solution. — 

18 6 7 5 Explanation. — A gain of 35^ is a gain 

•^ ^ of .35 of the amount invested. Multiply- 

^ ^ ^ ' ^ ing the investment by 35 resfarded as hun- 

26025 

dredths, and pointing off two places at the 



$ 3 3 6.2 5 Ans. • ^ ^ c ^\. a ^ • ^-^ • • j 

right of the product gives the gam required. 

Or; a gain of 35^ is a gain of 135 on llOO, equal to a gain 

of $.35 on each II invested. Since the investment is 8,G7o 

times $1, the gain will be 8,675 times 1.35, or 13,036.25. 

Example 2. — If I gain §700 by the sale of a lot for which I paid 
§4,375, what do I gain per cent.? 

Solution. — 

1 Q — i6«;. Ans. Explanation. — Since on 

§ 4 3 7 5 ) § 7 0.0^ ^^^ 375 there is a gain of 1700, 

2 6 2 5 on $1 there is a gain of j-^j-^ 

of 1700, and on 1100 there 

is a gain of 100 times ^ ..^ g of 700. This is the same as -^yz 

of 100 times 1700, or 116. But a gain of |16 on |100 is a 

gain of 16^. 



2 



PEDAGOGICvS OF ARITHMETIC. 



73 



Example 3.— 

receive for it §1 

Solution. — 

$10 

.1 25) §1 264. 

1 



500 


7 50 



-By selling my house and lot at a gain of 12J^ I should 
,264.50 more than I paid for it. What did I pay for it ? 

116 Ans. Explanation. — Since 12^^, or. 125 
of the cost of the house is the gain, 
or 11,204.50, .001 of the cost is yfg- 
of the gain, or 110.116, and 1,000 
times this, or $10,11(3, is the entire 

cost required. This result is obtained by dividing $1,204.50 

by .125, as in ordinary div'ision of decimals. 

Example 4. — How much will a lathe catalogued at §850 bring if sold 
at a discount of 40;?:, 20,'?:, and lOf^ ? 

Solution.— §850 X (1-00 - .40) X (1.00 -.20) X (1.00 -.10) 
= §850 X .6 X .8 X .9 = §367.20. Ans. 

Explanation. — If the lathe catalogtied at 1850 were gold 
at a discount of 40^, it would bring . 6 of $850 ; if this price 
were reduced 20^, the amount received woitld be ,8 of .6 of 
$850; and if still another reduction amounting to 10,^ were 
made, the sum needed to pay for the lathe would be .9 of . 8 
of .6 of $850, which amounts to $307.20. It is clear that the 
operation is only a case of multiplication of decimals. 



64, The Method by Common Fractions. — This method 
has the advantages of being well adapted to oral analysis and 
of being easy to teach and to understand. The essential 
condition of using it easily and rapidly is that the student 
shall be perfectly familiar with all the aliquot parts of 100^ 
and their value as expressed in equivalent common fractions. 
These aliquot parts, certain of their multiples, and their 
equivalents are shown in the following table : 



4% = 


.04 = sV 


18|^ = 


.1875 = ^\ 


561/^ = 


.5625 


5% - 


.05 = ,V 


20^ = 


•3 = i 


60;^ = 


.6 


m = 


.0625 = ,V 


25^ = 


.25 = J 


621^ = 


.625 


8Xfo = 


.081 =,V 


^\\i = 


.3125 = j% 


66|^ = 


.661 


10^ = 


•1 = tV 


331^ = 


.331 = 1 


70^ = 


.7 


in% = 


•IH = \ 


?^l\fo = 


.375 = 1 


75:^ = 


.75 


m% = 


.125 = 1 


m = 


•4 = 1 


80;^ = 


.8 


14S^ = 


.14f = 4 


43f^ = 


.4375 = ,V 


831^ = 


.831 


i6k = 


•16| - \ 


50jg = 


.5 =1 


8n% = 


.875 



7-t PEDAGOGICS OF ARITHMETIC. g 2 

Some of the parts given above are not much used either in 
decimal or in fractional form, yet it is of some importance 
that the teacher, if not the pupil, should be familiar with 
them. The manner of using them may be seen from the 
following examples: 

Example 1. — A man sold a horse for !S130, losing by the transaction 
iy|^'. What par cent, would he have gained if he had sold it 
for §180 ? 

Analysis. — Since he lost 1S^%, or j\r of the cost of the horse, he must 
have sold it for ^| of the cost. Then $130 is || of the cost; y\ of the 
cost is yig of §130, or §10, and the cost is 16 times §10, or §160. If he 
had sold it for §180, he would have gained on §160, the cost, the differ- 
ence between §180 and §160, or §20. If on §160 there is a gain of §20, 
on §1 there is a gain of ^i^ of §20, or §^-/^, equal to §J . A gain of | on 1 
is a gain of 121%. 

•ExAMPLK 2. — For how much must a sleigh that cost §275 be sold to 
gain 20,'? ? 

Analysis. — A gain of 20$^ is a gain of J of the cost; i of §275 
is §55 ; this added to §275, the cost, gives §330, the selling price 
required. 

Example 3.-^1 sold my house at a loss of 37^^/, receiving for it only 
$5,500; find its cost. 

Analysis. — To lose 371;^ is to lose f of the cost. Hence, I received 
f of -the cost of the house. This being §5,500, i of the cost is l of §5,500, 
or $1,100; and the cost is, therefore, 8 times $1,100, or §8,800. 

Example 4. — A dealer sold two stoves at $30 each; on one he 
lost 20j?, and on the other he gained 20rf. Did he gain or lose, and how 
much ? 

Analysis. — He lost 20;?, or J on one stove; he therefore received for 
it I of its cost. Hence, $30 was 4 of the cost of that stove ; i of its cost 
was 1 of $30, or $7i, and its cost, |, was 5 times $7i, or §37i. By selling 
the other stove for $30 he gained 20^, or ^ of its cost. The amount 
received for it, §30, was f of its cost ; i of §30, or §5, was i of the cost, 
and the cost, |, was 5 times §5, or $25. Since he received for them 
$30 + $30, or $60, and paid for them $37| + §25, or $62i, he lost 
§621 -$60 or $2 J. 

These examples are sufficient to show how readily the 
cases of percentage may be resolved by the method of 
analysis. 



§ 2 PEDAGOGICS OF ARITHMETIC. 75 

65. The Method hy P'orniulas. — This method of per- 
centage rec[uires only a slight knowledge of the equation, 
and this knowledge, on account of its extreme value in prac- 
tical computation, should be acquired as early as possible. 
In reducing formulated operations to their simplest numer- 
ical expression, cancelation is almost indispensable. The 
method of solving examples in percentage by means of 
formulas has, therefore, the effect of making pupils expert 
in cancelation, an operation that is too mvich neglected in 
school work. It is both interesting and instructive to derive 
from the fundamental formula the formulas covering the 
other cases. The process is very simple — so much so that 
the operation is easily within the mental scope of average 
pupils. 

From the formula, 

BxK 
100 ' ^^ 

by multiplying both sides by 100, we have 
100/^ = ^XA'; 



whence, 



n 1(10 7^ 


{^) 


100 P 

\ — 


i'^) 



and 



It is scarcely necessary to say that 

/>' = the base, or the sum on which the percentage is 
reckoned ; 

P — the percentage ; 

A' = the rate per hundred. 

If .^ = B-\-P, and B = B-P, by substituting in (1), 

xve have A = (I"^ + A)x/>- ^ ^^^ amount, (4) 

100 ' \ f 

and n = (lOO-A)xA^ ^ ^j^^ difference. (5) 

100 ' ^ ^ 

To illustrate the use of these formulas, a few examples 
will now be solved. 



76 PEDAGOGICS OF ARITHMETIC. § 3 

Example 1. — A man buys a lot for $900 and sells it at a gain of 15%. 
Find his gain. 

9 
900 V 15 
Substituting in (1), P = -.Q. = $135. Ans. 

Example 2. — If I gain §720 by selling a property at an advance of 8%, 
how much did I pay for it ? 

90 

Substituting in (2), B = ""^ ^ ^^^ = $9,000. Ans. 

Example 3. — At how much gain per cent, must I sell a house that 
cost $8,000 to gain $480 ? 

6 

Substituting in (3), J^ = ""^o ]^,,f^ = 6j^. Ans. 

Example 4. — I paid $8,450 for a property and s :)ld it at a loss of 1Q%. 
What did I receive for it ? 

Here we use formula (5), JJ = ^- r-- . 

Substituting. ^^^^ ~ \y ^'^''''^ = .84 X $8,450 = $7,098. Ans. 

66. Serial Discounts. — Within recent years it has 
become customary among business men to allow discounts 
in series such as 30^, 20fc, and 10^; 20^, 10^, and 5^; etc. 
The reason for this is that a discount so specified is really 
less than it seems. Thus, the first serial discount given 
above is not 30^ + ''^0^ + 10^) oi' QO^; in reality it is only 
49.6^. Similarly, the series 40^, 30^, 20 fo, and 10 fc, which 
seems to be 100^, is only 69.76^. A serial discoimt, say of 
20^, dOfc, and 25,^ is interpreted thus: 20^ of the full price, 
100^, is first deducted, leaving 80;^ of it. Then, 30^ of this 
80^, amounting to 24;^ of the entire price. Subtracting 24^ 
from 80^ leaves a remainder of 56^. Finally, 25^ of 56^ of 
the price is 14^ of it; these three reductions, instead of 
being 20^, 30^, and 25fo, or 75^, are really 20fc, 24^, and 14^, 
or 58^ of the price. 

Perhaps the best way to find the cost of an article on 
which a series of discounts is allowed is to find the continued 
product of the unreduced price and the remainders obtained 
by subtracting each of the several discounts from 100^. This 
may be shown by an example. 



§ 2 PEDAGOGICS OF ARITHMETIC. 77 

Example. — What must be paid, after a serial discount of 30$^, 25;?, 20;?, 
and 10;?;, for a piano of which the " long," or catalogue, price is $800 ? 

Solution.— §800 X -^ X -75 X -80 X .90 = $302.40. Ans. 
Or, $800 X t\f X I X t X t'u = $302.40. 

Explanation. — If the discount were oOfc, the cost would 
be 70^ of $800; if 25fo of this were thrown off, the remainder 
would be $800 X. 7 X. 75; if 20;^ of this were deducted, the 
remainder would be 1800 X . 7 X . 75 X . 8, and so on, as is shown 
in the solution. 

In order to find the single per cent, that is equivalent to a 
serial discount, it is evident that if the several remainders, 
obtained by subtracting from 1.00 the hundredths expressed 
by each discount in the series, be multiplied together, the 
resulting product will denote the hundredths that are to 
remain after the discount is dediicted. It is necessary, 
therefore, only to take this product from 1.00, and change 
the remainder into the corresponding per cent. Thus, let 
it be required to find the per cent, of discount that is equiv- 
alent to a serial discount of 30^, 25^, 20^, 10^, and 5^. 

(1.00 - .3)(1.00 - .25)(1.00 - .2) (1.00- . 1)(1.00 - .05) 

= .7X.75X.8X.9X. 95 = .3501; 1. 00-. 3591 = .0409 

= 64.09^. Ans. 

67. Applications of Pei'centag:e. — The applications 
of percentage are very extensive. This fact is owing to 
the great convenience of computations on the basis of one 
hundred. These different applications take many names 
in textbooks on arithmetic, but notwithstanding the inany 
names, examples illustrating the various applications may 
all be solved as cases of pure percentage. Moreover, these 
applications may all be included under two general classes: 

1. Applications not including the clement of time. 



{a) 


Profit and Loss. 


{<-') 


Brokerage. 


{l>) 


Stocks and Bonds. 


(/) 


Insurance. 


{c) 


Premium and Dis- 


{g) 


Taxes. 




count. 


{h) 


Duties and Customs. 


{d) 


Commission. 


(0 


Stock Investments. 



78 PEDAGOGICS OF ARITHMETIC. § 2 

2. Applications including the element of time. 

Equation of Payments. 
Averaging of Accounts. 
Compound Interest. 
Annuities. 



No two books can, perhaps, be found that will agree with 
respect to these names, but most arithmetics contain under 
some name all the foregoing applications of percentage. 



('0 


vSimple Interest. 


(/) 


(^) 


Partial Payments. 


{s) 


(0 


Discount. 


{h) 


{d) 


Banking. 


(0 


(0 


Exchange. 





INTEREST. 

68. Formulas. — If, in the formulas of percentage, the 
element R be resolved into r /, in which r denotes the annual 
rate and / the time in years, we obtain the formulas for every 
case in interest. 

The fundamental formula is 

Prt 

' = w <') 

Multiplying both sides of this by 100, and dividing as in 
percentage, we obtain 

rt ' ^^ 



100 / 
100/ 

TV- 



(3) 



(4) 



For A and D, by remembering in ( 1 ) that A — P-\- /, and 
that D = P— /, we have 

"^ - — 100 ' ^^^ 

and D = ^^— — . (6) 



§ 2 PEDAGOGICS OF ARITHMETIC. 70 

(>9. Use of tlio Foriuulas. — 

Example 1. — Find the interest of $:-J,0()0 for 2 years 5 montlis 18 days 
at 3^. 

Solution. — 2 years 5 months 18 days = 3 years + -/j year + ._}jj year 
= 2/5, or f i years. 

$3,000X3X 37 _ 

100 X 15 ~ ■ 

Example 3. — What principal in 3 years 3 months 15 days will give 
$790 interest at 8^^ ? 

100 X §790 X 34 ^.., ,,,,^ . 

Solution.— F = ^ — ^ — = $3,000. Ans. 

79 X 8 

Example 3. — At what rate will §4,000 in 3 years 8 months 34 days 
give §656 interest ? 

100 X §656 X 15 ^ , 
Solution.— r = ,. r\ ,^ — ^^ — = 6. Ans. 
§4,000X41 

Example 4.— In what time will §800 at 5fi give §90 interest ? 

„ . 100 X §90 .. ,, .3 ^, . 

Solution. — / = i^ttt^. ^ = 3| vears = 3 years 3 months. Ans. 

§800 X 5 ^ ' ^ 

70. The Six-Pei'-Cent. Method. — If it were not for its 

inaccuracy, there could be no more satisfactory method of 
computing interest than this. In spite of its incorrectness, 
its adoption originally Avas doubtless owing to its simplicity. 
But the calculations relative to every form of business are 
each year becoming more and more exact, and it will proba- 
bly not be very long until the six-per-cent. method will be 
dropped from our textbooks. Computations of every kind 
are being made a simple matter of reference to tables. To 
ascertain the exact number of days in any period less than a 
year, and to regard the result as so many 865ths of a common 
year, or as so many 36()ths of a leap year, will undoubtedly 
be the method of the early future. The teacher should 
therefore take particular pains to have the pupils expert in 
the method employed by the government. When the time is 
an exact number of years, all methods are alike correct. It 
is only when the time is expressed in months and days that 
inaccuracy results. If interest is to be computed for a period 



80 PEDAGOGICS OF ARITHMETIC. § 2 

extending through February of a leap year, the time should 
be regarded as part of a leap year. 

But in spite of the inexactness of the six-per-cent. method, 
it is yet in very general use, and it should therefore be thor- 
oughly mastered by pupils. In finding the multiplier there 
is no better way than to multiply 6 cents by the number 
of years, 5 mills by the number of months, and i of a mill 
by the number of days, and then take the sum of the 
products. This will give the interest at 6^ of II for the 
given time. It is then necessary only to multiply this 
sum by the number denoting how many dollars are in the 
principal. 

Example 1. — Find the interest at 6^ of $468 for 3 yr. 5 mo. 24 da. 
Also of $897.87 at the same rate for 5 yr. 11 mo. 29 da. 

Solution. — 

$.0(;x3 = $.1 8 
.005X5 = .0 2 5 
.OOOi X 24 = .004 

$.2 9 X 468 = $97,812. Ans. 
Solution. — 

$.06X5 = $.3 
.005X11 = .0 5 5 
.OOOi X 29 = .0 4f 

$.3 5 9 I X 397.87 = $143.17. Ans. 

If pupils be exercised in finding these multipliers until 
they can do it c|uickly and accurately, it is better than that 
they should be required to find them and use them with some 
principal. For their first operations in calculating interest 
will be found to contain many errors, and these will usually 
occur in the multiplier. They should therefore be at first 
required to solve many examples like the following: 

Example 2.— Find the interest of $1 at Q% for 3 yr. 7 mo. 18 da. 
Also for 1 yr. 4 mo. 14 da. 

Solution. — 

$.06X1 = $.0 6 
.005 X 4 =.0 2 
.0001X14 = .0021 
.2 18. Ans. $.0 8 21 Ans. 



Solution. — 




$.06 X 3 
.005 X 7 = 
.OOOi X 18 = 


= $.18 
= .0 3 5 
= .003 



§ 2 PEDAGOGICS OF ARITHMETIC. 81 

Explanation. — If the interest of II for 1 year is I.OfJ, 
for 3 years it 3 times $.06, or 1.18. Since the interest 
of II for 13 months is G cents, or GO mills, for 1 month 
it is ^ of GO mills, or 1.005, and for 7 months it is 7 
times $.005, or 1.03*5. Since the interest for 30 days is 
5 mills, for 1 day it is ^^ of 5 mills, or -£-^ mills, equal to 
|.000-|-. For 18 days the interest is 18 times i of a mill, 
or $.003. 

An explanation or analysis like the foregoing should 
be required until every pupil can give it correctly and 
without hesitation. After facility has been attained in 
calculating interest at 6^, interest at rates other than G 
should be taken up and practiced until rapidity and 
accuracy have been attained. iMost textbooks direct that 
in finding the interest at some other rate than G, the 
student shall divide by G and multiply by the given rate. 
This is not usually the best order, for fractions are likely 
to occur that may be avoided if the interest at Qfo is first 
multiplied by the given rate and the product be then 
divided by 6. This will appear in the solution of the 
following example : 

.Example 3. — By the six-per-cenl. method find the interest of $317.50 
for 2 yr. 7 mo. 21 da. at 5h%. 

Solution. — 

$.06 X 2 = $.1 2 §.1585X317.5 = §50.32+ 



.005 X 7= .0 3 5 $50.32h-6 = $8.38| 

.000^X21= .0035 $8.38f X 51 = §46.13 



i (•) 



$.15 8 5 $50.32 X 5h = $276.76 ( 

§276.76 H- 6 = §46.13 f ^"' 

Explanation. — The student will notice that in (1) 150.32 
divided by G we obtain a mixed number for a quotient, and 
that this mixed number must be multiplied by another mixed 
number. If, however, we first multiply by 5i and afterwards 
divide by 6, the fractional difficulty is in a large measure 
avoided. 

When the multiplier itself is exactly divisible by 6, or 
when the principal is, it is better to change either the one or 
the other before finding the required interest. 



82 PEDAGOGICS OF ARITHMETIC. § 2 

est of $240 for o yr. <S mo. 13 da. 



S.222 X 240 = $53.28 | 

$53.28 X 4.1 -=- 6 = $39.96 f ^ ' 



EXAMri.E 


4.- 


-Fin 


id the • 


at 4^%. 










Solution. 


— 








$.06 


X 


3 = 


$.18 




.005 


X 


8 = 


.0 4 




.000^X1 


12 = 


.0 2 



240--6x4\ ~ 180 I 
§.2 2 2 $.222X180'= $39.96) 

§.222h-6x4J = $.1665/ 
$.1665X240 '= $39.96 )' 



(2) 



The foregoing- illustrates three methods of procedure. 
The first is the one usually employed — to find the interest 
at (jfo and then derive from that the interest at 4|-^. In (2) 
advantage is taken of the fact that 240 is a multiple of (i, 
and (3) the divisibility of -11^.222 by 6 is utilized. 

71. The Method by Aliquot Parts. — For periods 
greater than a year, many teachers prefer the method of 
finding interest by aliquot parts. It is as available for one 
rate as it is for another, but has the divSad vantages of being 
somewhat longer and more liable to error than the six-per- 
cent, method. Like the latter method it assumes the year 
to consist of 12 months of 30 days each. A few examples 
will show its method of procedure. 

ExAMPi.K 1.— Find the interest of $324.60 at 3|^ for 3 yr. 11 mo. 12 da. 
Also the interest at 5^% of $79.48 for 1 yr. 5 mo. 20 da. 

Solution.— $ 3 2 4.6 
.031 



1 2.1 7 25 = int. fori yr. 

2 4.34 5 = •' '■ 2 '" 
6.08625 = " " 6 mo. 
3.043 125=" " 3 " 
2.0287 5 = " " 2 " 

.4057 5 = " •' 1 2da. = iof 2mo. 



$4 8.08 137 5 = " " 3yr. 1 1 mo. 1 2da. 



Solution.— $7 9.4 8 
.0 5 J 



$4.37 14 = int. fori yr. 

1.4 57 1 3 = " " 4 mo. 

.36428 = " "1 " 

.12 143= " "1 Oda. 

.12 143 = " '• 1 " 

$6.435 67= " " 1 yr. 5 nio. 2 da. 



2 



PEDAGOGICS OF ARITHMETIC. 



83 



Explanation. — We first find the interest of $324.60 for 

I year at 3f^. If this be doubled the sum of the two will be 
the interest for 3 years. To find the interest for 11 months 
we take half of 1 year's interest, or 6 months' interest, ^ of 
6 months' interest, , or 3 months' interest, and then ^ of 
6 months' interest, or 2 months' interest. The sum of these 
three interests is the interest for G + 3 + 3 months, equal to 

II months. It remains to find the interest for 12 days. vSince 
12 days is |- of 2 months or 60 days, we divide the interest 
for 2 months by 5. Adding these separate amounts we 
have the interest required. 

In the second example, we find the interest for 1 year, 
take ^ of it, then ^ of 1 months' interest, and finally, i of 
1 month's interest, writing it twice. The sum of all these 
is the interest for 1 yr. 5 mo. 20 da. 

EX.A.MPLE 2.— What is the interest of §4,236.39 at 4^% for 5 yv. 10 mo. 
29 da.? Solve also by the six-per-ceiit. method. 

Solution. — 

$ 4 2 3 6.3 9 
.04# 



$ 2 3.3 4 6 7 2 = 


int. for 1 yr. 




8 13.3 8688 = 


" 


" 4 •' = 


4 times 1 yr. 


6 7.7 8 2 24 = 


•' 


4 mo. = 


i of 1 ■' 


6 7.7 8 2 24 = 


" 


" 4 •' = 


i " 1 " 


3 3.8 9 1 1 2 = 


" 


" 2 " = 


h " 4 mo 


11.2 9 704 = 


" 


" 2 da. = 


i •' 2 " 


2.8 24 2 6 = 


" 


" 5 " = 


i " 20 da. 


2.2 5 94 1 = 


" 


" 4 " = 


1 " 20 •• 


^1202.569 9 1 = 


" 


" 5 yr. 1 


mo. 2 9 da. 


Solution. — 








1.06 


X 5 


= $.3 




.005 


xio 


= .0 5 




.0001 


X29 


= .004f 





S.3 5 4f 

.3541X4,236.39 = $1,503.212385 
1,503.212385 X 4.8 -f- 6 = $1,202.57 



12, The Sixty-Day Method.— The following method 
may be employed very advantageously for periods less 



84 PEDAGOGICS OF ARITHMETIC. § 2 

than 1 year, whether the time be expressed in days, or in 
months and days. By the ordinary method of computing 
interest, 12 months of 3U days each, or 3 GO days, are taken 
as 1 year; so that 2 months — 60 days — must be regarded 
as |- of a year. Hence, when the rate is Qfo a year, that is, 
when .06 of the principal equals the interest for 12 months, 
or 360 days, .01 of the principal will be the interest for 
2 months, or 60 days. But .01 of any sum is found by moving 
the decimal point two places to the left. Thus, the interest 
at Gfc for 60 days of $4,795 is 147.95 ; of 1369.50 it is 13.695. 
That is, 

77/r interest of any principal for 2 months, or GO days, at 
6<fo is .01 of that principal, and is found by moving the point 
between dollars and coits two places to the lejt. 

If the time is either more or less than 60 days, the required 
interest may be found by the method of aliquot parts ; and, 
if the rate is other than 6^, the interest at the rate given 
may be found in the same way. 

Example 1.— Find the interest of §60,000 for 46 days at 6;?; also of 
$8,469.24 for 119 days at the same rate. 

Solution. — Solution. — 

$ 6 0.0 = int. for 6 da. $ 8 4.6 9 2 4 = int. for 6 da. 

3 0.00= " " 30 " 42.3462= " " 30 

15 0.00= "" 15 •' 28.2308 = 

10.0 = " " 1 '. 8.4692 = 

4.2 3 46 = 



4 6 0.0 = " " 4 6 da. 



1 6 7.9 7 3 3 = 



20 
6 

3 

1 1 9 



Example 2.— Find the interest of $36,759.60 for 237 days at 5A^; also 
of $7,500 for 8 months 29 days at 4^?/. 

Solution. — 

$3 6 7,5 9 6 = int. for 6 da. 

7 3 5.1 92 = " "120" 

18 3.798 = " " 30 " 

1 2 2.53 2 = " " 2 " 

30.6 33 =" " 5 " 

1 2.2 5 3 = " " 2 " 



1 2)$ 1452.004 = " "2 37 
1 2 1.0 = int. at \% 
$1 33 1.00 4 = " ' 5^^ 



2 PEDAGOGICS OF ARITHMETIC. 

Solution. — 

$ 7 5.0 = int. for 2 mo., or 60 da. 



2 2 5.0 = 

2 5.0 = 
2.5 = 
7.5 = 
1.2 5 = 



4) $3 3 6.2 5 = 



6 " 
2 da. 
2 " 
6 " 
1 " 



8 mo. 2 i) da. 



8 4.06 = 1 of 6^, or l.l^int. 



$2 5 2.1 9 r= int. at 41^. 

KS. C\iangin^ from Interest at 6^ to Interest at 
Another Rate. — After interest at (jfc has been obtained, it 
is customary to divide this by (i and then to multiply the 
quotient by the given rate. It is usually better, however, 
to employ the method of aliquot parts, as in the examples 
above. Thus, if we have the interest at 6^, by taking away 
i of it, there will remain the interest at 5^; or if ^ of it be 
added, the sum will be the interest at 7i. By adding or 
subtracting I of the interest at G^, we obtain the interest, 
respectively, at Sfc or 4^. And so on for other integral rates. 
If the required rate is a mixed number, two or more opera- 
tions may be necessary. 

Example 1. — If the interest of a certain principal at 6j? is $237.60, 
what will be the interest at 3|^ when the principal and time are the 
same .-' 



Solution. 



2 ) $237.60 = int. at e^. 
1 1 8.8 = " " Sfc. 
2 6.4 = " " I of 6^, or l;^;. 



$1 45.20 = " " S?/o. 

Explanation. — It is clear that if the interest at 6^ be 
divided by 2, the quotient will be the interest at 3^. This 
quotient must now be increased by interest at f^. Since 
6 = L8^ it is evident that | is |- of 6. Hence, if to the inter- 
est at ofc we add | of the interest at 6^ we shall have the 
interest at 3|^. Again, it is often simpler to reduce both 
rates to improper fractions that have equal denominators, 
and then apply the method of aliquot parts. Let us do so 
in this case. Gfo = -L^^; 3|^ = Jgi^. The problem now is to 



86 PEDAGOGICS OF ARITHMETIC. § 2 

find 11 by the method of aliquot parts when we know 18. 
There are three steps : 

18-^2 = 9; 18-^9 = 2; 9 + 2 = 11. 

Example 2. — If the interest of a certain principal at 6% is $123.45, 
what is the interest at 2^% ? at 3|$* ? 

Solution. — 

4, 9 ) $ 1 2 3.4 5 = Q'^, or -\H. 

3 0.8625 = ^oi-Y-fc, or |$?. 
13.7 17 = i-'V-^, " 1%. 
13.7 1 7 = " " " " " II 



Solution. — 



$ 5 8.2 9 6 = 2|^, or \^-fc. 

2 ) $1 23.4 5 = V-^. 

4 ) 6 1.7 2 5 = -\^-%. 
1 5.4 3 1 = 1%. 

$77,156 = V^, or3f^. 

74. Exact Interest. — The common method of com- 
puting interest, in which 12 months of 30 days each are 
regarded as a year, is gradually being discarded for the more 
accurate process of exact interest. Both the United States 
and the English governments have abandoned the usual 
plan of assuming the year to be composed of 360 days. The 
interest on all government obligations is found by treating 
the common year as composed of 365 days, and the leap year 
of 366 days. There is little doubt that every department of 
business will soon estimate the year in the same way as the 
government now does. 

If the time for which accurate interest is to be computed 
begins in a year next preceding a leap year, and extends 
beyond February 29 following, the time should be counted 
as so many 366ths of a year. When the years for which 
interest is computed are a whole number, of course, there is 
no difference between exact interest and ordinary interest ; 
but when months indiscriminately are regarded as com- 
posed of 30 days, the interest for any part of an ordinary 
year is 3^5, or -7^3, too much, and for a leap year 3! g-, or -^^y, 
more than it should be. If there is a form of interest that 
should engage the attention of the teacher, it is this. 



§ 2 PEDAGOGICS OF ARITHMETIC. 87 

Example 1. — Find the exact interest of §7,300 at 6;^ for 60 days of an 
ordinary year. 
Solution. — 

7 3 ) $ 7 3.0 = int. for 60 days at 6^, by ordinary method. 
1.0 = deduction. 

$ 7 2.0 = exact interest for g'^g'V of a year. 

Example 3. — Find the exact interest of §83,924 for 97 days of an 
ordinary year at 5^%. With the same data find the interest on the sup- 
position that the year contains 866 days. 

Solution.— $ 8 3 9.2 4 = int. for 6 da. 

4 1 9.6 2 = " " 30 " 

6 9.937 = " " 5 " 

13.987 = " " 1 " 

18.987 = " " 1 " 



12)1185 6.771 = " " 9 7at6$r. 

1 1 3.0 6 4 = " " " " l^. 

73)$ 1 243.70 7 = " " " " 51%. 

1 7.0 3 7 = deduction. 

§ 1 2 2 6.6 7 = exact int. for 97 days at 5|^. 

Assuming the year to contain 366 days, the deduction will be J^ of 
the interest as found by the ordinary method. Thus, 

61) $124 3. 707 = int. at 5i% by ordinary method. 
2 0.3 8 8 = deduction. 
$122 3. 319 = exact interest. 

Example 3.— Find the exact interest at 'd\fc of $68,928.80 from Octo- 
ber 23, 1899, to July 4, 1900; also, from January 19, 1904, to November 
10, 1904, at 4|^. 

Note. — July 4 being a legal holiday, the time is counted to July 3. 

Solution. — 

.S68 928 80 y -— V ~ — "^ ' ' — SI 672 23 Ans 

7 2Qfi 
Solution.— $68,928.80 X-Lx^ = $1,951.10. Ans. 
200 000 

75. Annual Interest. — This is a method of calculating' 
interest closely allied to compound interest. In many of the 
states it is contrary to law. This, probably, is the reason that 
the subject is ignored by many textbooks on arithmetic. In 
order to collect annual interest in any state where it is per- 
mitted, it must be mentioned in legal form that interest is 
payable annually. 



88 PEDAGOGICS OF ARITHMETIC. § 2 

Example.— Find the amount of a debt of §4,000 in 5^ years at 6%. 
interest payable annually, assuming that no payment is made until the 
end of the period. 

Solution.— Interest of $4,000, at 6%, in 5^ years = $1,320. 

Interest of $4,000 for 1 year = $240. 

The first year's interest remains unpaid 4.^ years, the second, 
3.V years, the third, 2^ years, the fourth, 1\, and the fifth, ?,. So that 
the interest of $240 is due and unpaid for 4^ + 3^ - + 21 + H + J, or 
121 years. This interest will be $180. 

Hence, the required amount will be $4,000 + $1,320 + $180, or $5,500. 

76. Conii)oiind Interest. — As the result of competi- 
tion, compound interest is allowed by many savings banks, 
although it is illegal. Adopting the foregoing notation, and 
assuming that the interest is compounded annually, we shall 
have for the amount at the end of one year, 

A = 7^(1.00 + r), 

in which r is to be understood as hundredths. At the end of 
two years, 

A = 7^(1.00 + ;-) (1.00 + ;-) = P (1.00 + /-)=. 
Hence, generally, the formula for A in / years is 
A = P (1.00 + ;-)'. 

If the interest be added to the principal more frequently 
than once a year, r in the formula will become the same part 
of the annual rate as the period is of one year. Thus, if the 
annual rate is 8^, and tlie interest is compounded quarterly, 
r in the formula becomes .02. It is more convenient in com- 
puting compound interest to employ the tables that are to be 
found in nearly all arithmetics. 

77. Partial Payineuts. — There are several rules for 
computing interest on obligations discharged by partial pay- 
ments. The most commonly used of these rules are the 
United States Rule legalized by the vSupreme Court of the 
United States, and the Merchants Rule. 

Two other rules are frequently given in the textbooks; 
they are the Vermont Rule and the Connecticut Rule. 
These, however, are but little used among business men, 
and only in the states whose names they bear. 



§ 2 PEDAGOGICS OF ARITHMETIC. 89 

United States Rule for Partial Pa;rnients. — Fi)id tJic 
anion lit of t/ic principal to the time luhoi the payment, or the 
snni of tzuo or more payments, is greater than the interest 
then dne. From this amount snbtracf the payment, or the 
snm of the payments, and treat the remainder as a net^' prin- 
cipal. Proceed in this manner to the date of settlement, and 
the last amount will be the sum still due. 

The student will notice that no payment on account is per- 
mitted to reduce the amount of an interest-bearing obligation 
unless the payment is large enough to discharge the interest 
on the obligation up to the time when the payment is made, 
and to pay something on the principal besides. Thus, if I 
lend 1100 at iyfc interest on condition that the debt, principal 
and interest, is to be paid at intervals and in amounts to suit 
the convenience of the borrower, this would be a case of par- 
tial payments. Now, if at the end of G months, when the 
accrued interest is #3, the borrower pays me 12 or 13 on 
account, the payment is credited, of course, but it does not 
change the amount that draws interest. But if the payment 
is 15, then 13 of this is used to pay the interest and the 
remaining -$2 reduces the principal to 198. 

This really allows the debtor interest not on each entire 
payment, but on its excess above the interest accrued at the 
time the payment is made. Or, if several payments, taken 
separately, are each less than such accrued interest, but taken 
together they exceed the interest accrued at the time when 
the last payment is made, their sum is to be used exactly as if 
it were one payment greater than the accrued interest. The 
Merchants Rule is more advantageous to the borrower than 
the United States Rule, for he receives interest on each entire 
payment from the time it is made until the date of .settlement. 

Mercliants Rule for Partial Payments. — Find the 
amount {usuallv by the method for computi)ig exact interest) 
of each of the several payments from the time it is made to the 
time of settlement. Subtract the sum of these amounts from 
the amount of the obligation from its date to the time of set- 
tlement. The remainder luill be the sum still due. 



90 PEDAGOGICS OF ARITHMETIC. § 2 

This rule puts upon both the lender and the borrower the 
necessity of paying interest for money received by either 
from the other, and of doing so for every sum, large or small. 
We shall now illustrate these rules by an example. 

Example. — A note for §2,400 bearing interest at Q% was dated Jan. 1, 
1900, and had the following indorsements for payments made on account: 
May 23, 1900, §25; Sept. 17, 1900, §50; Dec. 20, 1900, $480; Apr. 28, 1901, 
§650 ; July 6, 1901, §800. What was due Jan. 1, 1902 ? 

Solution. — The following is according to the United States Rule. 

Principal §2400.00 

Int. from Jan. 1 to Dec. 20, 1900 (11 mo. 19 da.) 139.60 

Am't due Dec. 20, 1900 §2539.60 

Payments that together exceed the interest (§25 + §50 + §480) . 555.00 

New prin. Dec. 20, 1900 §1984.60 

Int. from Dec. 20, 1900, to Apr. 28, 1901 (4 mo. 8 da.) 42.34 

Am't due Apr. 28, 1901 §2026. 94 

Fourth payment 650.00 

New prin. Apr. 28, 1901 §1376.94 

Int. from Apr. 28, 1901, to July 6, 1901 (2 mo. 8 da.) 15.61 

Am't due July 6, 1901 §1392.55 

Last payment 800 . 00 

New prin. July 6, 1901 §592.55 

Int. from July 6, 1901, to Jan. 1, 1902 (5 mo. 25 da.) 17.28 

Am't due at settlement, Jan. 1, 1902 §609.83 

Solution. — The following is according to Merchants Rule, exact 
interest : 

Principal §2400.00 

Int. from Jan. 1, 1900, to Jan. 1, 1902 (2 yr.) 288.00 

Am't of prin. at time of settlement §2688.00 

Am't of §25 from May 23, 1900, to Jan. 1, 1902 (1 yr. 

223 da.) §27.42 

Am't of §50 from Sept. 17, 1900, to Jan. 1, 1902 (1 yr. 

106 da. ) 53 . 87 

Am't of §480 from Dec. 20, 1900, to Jan. 1, 1902 (1 yr. 

12 da.) 509. 75 

Am't of §650 from Apr. 28, 1901, to Jan. 1, 1902 (248 da.). 676.50 
Am't of $800 from July 6, 1901, to Jan. 1, 1902 (179 da.). 823.54 

Am't of payments §2091.0 8 

Bal. due at settlement §596.93 



§ 2 PEDAGOGICS OF ARITHMETIC. 91 

Solution. — The following is according to Merchants Rule, six-per- 
cent, method: 

Am't of principal at settlement S'2688.00 

Am't of $25 from May 26, 1900, to Jan. 1, 1902 (1 yr. 

7 mo. 8 da. ) §27.41 

Am't of $50 from Sept. 17, 1900, to Jan. 1, 1902 (1 yr. 

3 mo. 14 da.) 58.87 

Am't of §480 from Dec. 20, 1900, to Jan. 1, 1902 (1 yr. 

11 da.) 509.68 

Am't of §650 from Apr. 28, 1901, to Jan. 1, 1902 (8 mo. 

3 da.) 676.33 

Am't of §800 from July 6, 1901, to Jan. 1, 1902 (o mo. 

25 da.) ' .' 823.33 

Am't of payments §2090.62 

Bal. due at settlement §597 . 38 

78. Difference in the Results by Tliese Rules. — The 

student will, doubtless, be surprised at the very considerable 
difference between the amounts due at settlement of the fore- 
going- obligation. By the United States Rule the amount 
still owing is |609. 83, and by the Merchants Rule it is only 
1597.38 when interest is computed by the six-per-cent. 
method. This difference is $12.45, and at first thought it 
might seem that no such difference is possible, and that an 
error has been made in the calculation. Such is not the case, 
however. The greater cost to the debtor when interest is 
calculated by the United States Rule is due to the fact that 
he loses the interest on such part of each payment as is used 
to discharge the interest accrued at the time the payment is 
made, and that he loses this from that time until the time of 
settlement. Besides this loss, the debtor loses the interest 
on any payment that is neglected because it is less than the 
accrued interest at the time the payment is made. This loss 
is the interest on such payment from the time it is made imtil 
a payment is made that is not so neglected. From these two 
sources the sum of losses to the borrower should be equal to 
the difference between the results by the two methods. It 
is important that this matter should be very clearly under- 
stood by the teacher, and when the age and intelligence of 
classes will admit, it should be mastered in the classroom. 



92 PEDAGOGICS OF ARITHMETIC. § 2 

The Merchants Rule assumes that the money of the bor- 
rower is as much entitled to interest as the money of the 
lender, and it requires that when two men are paying money 
to each other, either as loan or in repayment of loan, interest 
must be computed on every sum from the time it is paid 
until the time of settlement. This seems perfectly equitable, 
and if it is, the United States Rule is not so. At any 
rate, if one pays a debt by the method of partial payments, 
he will do well to insist on applying the Merchants Rule 
in settlement. The lender, however, if he is perfectly 
familiar with the two methods, will prefer the United States 
Rule. 

79. Short Methods for Sijecial Cases. — The following 
will be found to be excellent rules for finding the interest on 
any principal for any number of days. When the principal 
contains cents, to express the interest in dollars and cents, 
point o£E four places from the right of all results obtained 
by the rules that follow. When the principal contains dollars 
only, point off two places. 

Four Per Cent. — Multiply the principal by the number of 
days to rim, and divide by 00. 

Five Per Cent. — Multiply the principal by number of days, 
and divide by 72. 

Si.v Per Cent. — Multiply the principal by number of days, 
and divide by 00. 

Seven Per Cent. — Multiply the principal by number of days, 
and divide by 52. 

Fight Per Cent. — Multiply the principal by number of days, 
and divide by 45. 

N^ine Per Cent. — Multiply the principal by number of days, 
and divide by 40. 

Ten Per Cent. — Multiply the principal by number of days, 
and divide by 3(). 

Twelve Per Cent. — IMultiply the principal by number of 
days, and divide by 30. 

Fifteen Per Cent. — Multiply the principal by number of 
days, and divide by 24. 



§ 2 PEDAGOGICS OF ARITHMETIC. 93 

EigJitcen Per Cent. — Multiply the principal by number of 
days, and divide by 20. 

Tivcnty Per Cent. — Multiply the principal by number of 
days, and divide by 18. 

Tzventy-foitr Per Cent. — Multiply the principal by number 
of days, and divide by 15. 

It should be noted that the foregoing rules, with the 
exception of that for 7 per cent., give the same results 
as would be obtained by the six-per-cent. method. The 
rule for 7 per cent, assumes that a year contains 304 
days. The result in this case is very nearly exact 
interest. 

80. Bank Discount and True Discount. — One of the 

most serious difficulties within the entire range of the appli- 
cations of percentage is to comprehend clearly the distinction 
between bank discount and true discount. 

Bank discount is the amount charged by a bank for advance 
payment of a note or other obligation. Thus, I may have 
A's note in which he promises to pay me, say -11,000, in 
3 months or 3 months or 30 days or any other period. If I 
keep the note until it is due, A will pay me what the note 
promises. But I may need the money now; if so, I can 
sell the note to a bank for somewhat less than it will be 
worth at the time it becomes due. The bank will hold 
the note until it matures and will then collect its face value 
from A. 

In determining the ainount to be paid for the note, the 
bank calculates the interest for the time that mtist elapse 
before the note is due, at the legal rate, on its face value. 
This time is usually increased by 3 days of graee, because in 
most states the man that owes a note is not compelled to pay 
it until 3 days after the time when it is nominally due. This 
interest is called diseonnt, and the difference between the 
sum mentioned in the note and this discount is called the 
proceeds. The proceeds of a note or other obligation is what 
is received for it by the one that sells it before it is due. 
Clearly then, bank discount is only a case of simple interest 



94 PEDAGOGICS OF ARITHMETIC. § 2 

in which the principal, rate, and time are given. The inequity 
of the operation consists in the fact that the bank charges 
interest not only on the amount paid for the note, — the pro- 
ceeds, — but also on the discount itself — the amount charged 
by the bank for advance payment. 

Illustration. — I wish to sell to a bank today A's note 
for 11,000 without interest, and due in CO days after today 
with grace. If money is worth Gfc, the bank will charge me 
for discounting the note, Gfo interest of 11,000 for 63 days. 

10001X03 = 10105; 10105x1,000 = $10.50, discount. 

11,000 — $10.50 = $989.50, proceeds. 

In strict equity, I should receive for my note a sum of 
money such that if it were put on interest today at 6^, it 
would amount to $1,000 in 63 days. Now we know that if 
$1 were thus placed on interest it would amount to $1.00 
+ $.0105, or $1.0105, in 63 days. Hence, I should receive for 
my note of $1,000 as many times $1 as $1.0105 is contained 
times in $1,000. 

$1,000 -^ $1.0105 = 989.61; $1X989.61 = $989.61, true 
proceeds. 

$1,000 -$989. 61 = $10.39, true discount. 

By the method employed in banks, I get as the proceeds 
of my note 11 cents less than I am entitled to receive. Now 
this 11 cents is the interest of $10.50 for 63 days at 6^; 
for $.0105x10.50 = $.11025. Since the sums discounted 
annually amount for some banks to many million dollars, it 
is clear that by their method of computation, their gains, to 
which they have no just claim, are very large. 



IXTEREST LAMS OF CANADA. 

In five provinces of Canada — namely, British Columbia, 
Manitoba, New Brunswick, Ontario, and Quebec — there is 
uniformly an established legal rate of 6^ with grace on notes, 
bills, and sight drafts. No penalty is exacted for usury, and 
any rate above 6^ may be agreed on by contract. In Nova 
Scotia grace is allowed and there is no fixed legal rate per 
cent. 



PEDAGOGICS OF ARITHMETIC. 



95 



INTEREST LAWS OF THE UNITED STATES. 

(Compiled from the ^''Bankers' Register.") 



States and 
Territories. 



-4 O 



Rate 

Allowed by 

Contract.' 

Per cent. 



Penalties for Usury. 



Grace 

or 

No Grace. 



Alabama 

Arizona 

Arkansas 

California 

Colorado (a) 

Connecticut 

Delaware 

Dist. of Columbia. . . 

Florida 

Georgia 

Idaho (b) 

Illinois 

Indiana 

Indian Territorj' 

Iowa (c) 

Kansas 

Kentucky 

Louisiana 

Maine (</) 

Maryland 

Massachusetts {e). . . 

Michigan 

Minnesota 

Mississippi 

Missouri 

Montana 

Nebraska 

Nevada 

New Hampshire (/) 

New Jersey 

New Mexico 

New York (g-) 

North Carolina (k).. 

North Dakota 

Ohio 

Oklahoma 

Oregon 

Pennsylvania 

Rhode' Island {e) 

South Carolina 

South Dakota 

Tennessee 

Texas 

Utah 

Vermont 

Virginia 

Washington 

West Virginia 

Wisconsin (/) 

Wyoming (/) 



Any rate. 

10 
Any rate. 
.■\ny fate. 

() 
10 
10 

8 
12 

7 

8 
10 

8 
10 

6 

8 
Anv rate. 


Any rate. 

8 
10 
10 

8 
Anv rate. 

10 
Any rate. 

6 

6 
12 

6 
12 

8 
12 
10 

(i 
Any rate. 

8 
12 

(i 

10 

Any rate. 

() 

(5 
12 

6 
10 
12 



Forfeiture of entire interest. 

None. 
Forfeiture of prin. and int. 

None. 
None, except pawnbrokers. 

None. 
Forfeiture of double the prin. 
Forfeiture of entire interest. 
Forfeiture of entire interest. 
Forfeiture of excess. 

Forfeiture of entire interest. 
Forfeiture of excess of int. 
Forfeiture of prin. and int. 
Forfeiture of int. and costs. 
Forfeiture of excess of int. 
No statute in force. 
Forfeiture of entire interest. 

None. 
Forfeiture of excess of int. 

None. 
Forfeiture of interest. 
Forfeiture of prin. and int. 
Forfeiture of all interest. 
Forfeiture of entire interest. 

None. 
Forfeiture of int. and cost. 

None. 
Forfeiture of thrice the excess. 
Forfeiture of int. and costs. 
Forf. twice am't and $100 fine. 
Forfeiture of prin. and int. 
Forfeiture twice am't paid. 
Forfeiture of entire interest. 
Forfeiture of excess above 8/?. 
Forfeiture of entire interest. 
Forfeiture of prin. and int. 
Forfeiture of excess of int. 

None. 
Forfeiture of double excess. 
Forfeiture of entire interest. 
Forfeiture of excess interest. 
Forfeiture of entire interest. 

None. 
Forfeiture of excess of int. 
Forfeiture of interest. 
Forf. from prin. double excess. 
Forfeiture of excess of int. 
Forfeiture of entire interest. 
Interest and costs. 



Grace. 

Grace. 

Grace. 
No grace. 
No grace. 
No grace. 
No grace. 
No grace. 
No grace. 

t 
No grace. 
No grace. 

(Jrace. 

G race. 

G race. 
t 

Grace. 
t 

No grace. 

Grace. 
Grace. 
Grace. 

t 

No grace. 

(irace. 

t 

No grace. 

(irace. 
No grace. 

Grace. 
No grace. 
No grace. 

Grace. 
No grace. 
No grace. 

Grace. 

Grace. 
No grace. 

Grace. 
No grace. 
No grace. 
No grace. 
No grace. 
No grace. 
No grace. 

Grace. 



+ Grace on notes and bills, but not on sight drafts. 

(a) By the laws of 1897 interest by pawnbrokers at more than Z% a month on the 
sum actually loaned involves a penalty of $l(Xt. 

(b) Loss of interest by tender; 10 per cent, from borrower for school fund. 

(c) Defendant forfeits also 10» a year to school fund. 

{d) On paper dated on or after July 1, 1897, no grace except on sight drafts. 
((') Grace on sight drafts, but not on IdIIIs and notes. 
(/) No grace tmless so agreed. 

(g) Contract void; punishable as misdemeanor. (On call loans of $5,000 or upwards, 
on collateral security, any rate of interest is legal.) 
(/r) No grace on demand paper. 

(/) Forfeiture entire interest, and treble excess paid recoverable. 
ij) Six per cent, on all state, county, and municipal bonds and warrants. 



96 PEDAGOGICS OF ARITHMETIC. g 2 



PROrORTIOJ^. 

81. Transfoi'iiiatioiis. — There is no subject in arithme- 
tic that should be more carefully taught than this. It should 
be shown that the ratios making up a proportion are funda- 
mentally derived from the fraction. 

Thus, f expresses the ratio of 3 to 5; and 3 : 5 = 6 : 10 is 
merely a derived form of f = y^^. In these days, w^hen the 
authorities in pedagogy are insisting upon the importance of 
correlation, this opportunity to correlate should not be neg- 
lected. Then, too, the principles employed in proportion 
are more obvious to the pupil if derived directly from the 
fraction. 

Thus, to show that the product of the means in a propor- 
tion equals the product of the extremes: 

A C 

^ = — is the same a.s A : B = C : B, in which A and D 

are extremes and B and C are means. Multiplying the frac- 
tions by B D, we have 

AD = BC. 

Dn. 



Again, if 


A 
B 


111 Cn , „ ^ 
— = -y^— , A Hi : B in = C n 
in D n 


But, 




A in A ^ C 11 C 
Bin - i>" """'^Z;// ~ D' 


whence, 




A \ B = C : D. 



Hence, citlicr ratio or both ratios of a simple proportion may 
be simplified by divieling. 

Thus, if 8 : 12 = 40 : 60, we may divide the first ratio by 
4 and the second by 20, and we obtain 

2:3 = 2:3. 

The ratios of a compound proportion may be simplified in 
the same manner. 

In a similar manner it may be shown that 

Both antecedents or both consequents may be divided — each 
pair by any number that will exactly divide its terms. 



§ 2 PEDAGOGICS OF ARITHMETIC. 97 

Thus, 8 : 12 = 40 : GO. If the antecedents be divided by 
8, we shall have 

1 : 12 = 5 : GO. 

If the consequents be divided by 12, we shall have 
8 : 1 = 40 : 5. 

If a proportion contains fractions, they may be removed by 
multiplication. 

Thus, 8i : 10 = 31 : 4. 

Multiplying the antecedents by 3, we have 
25 : 10 = 10 : 4. 

A great variety of transformations is possible with propor- 
tions without destroying them, and the ingenious teacher can 
advantageously use them all. If the pupils know something 
of algebra, they should be required to use it in discovering 
these transformations. 

It may here be remarked that the fractional form of stating 
a proportion is rapidly superseding the extended forin given 
above. Also, that the double colon, used to separate the two 
ratios, has been almost entirely discarded in favor of the sign 
of equality. Both of these changes are to be commended. 

82. Cause and Effect. — There is no method of stating 
a proportion, either simple or compound, in which the cor- 
rectness of the result may be relied upon with the same 
degree of certainty as this. It is an easy matter for the pupil 
to select the causes, and the effects produced by those causes. 
The exercise addresses itself to the judgment from a new 
standpoint, and thereby gains additional value. 

The principle upon which it depends is one of equilibrium. 

TJie product of tlic fii'st cause and the second effect equals 
that of the second cause and the first effect. 

This may be shown as follows: 

Example. — Let Ci and Ci denote the causes, and Ey and Ei the cor- 
responding effects. 

Then, ^ = ^. 

G E^ 

Clearing of fractions, dE-^ = C\Ei. 



9S PEDAGOGICS OF ARITHMETIC. § 2 

There are various forms in which examples are written for 
solution by this method, but the solution of the following 
example will serve to illustrate one of the best. The miss- 
ing term is denoted by x, and the canceling is across the 
vertical line. 

Example. — If 12 men dig a trench 40 rods long in 24 days of 10 hours 
each, how many rods (.r) can 16 men dig in 18 days of 9 hours each ? 

Here, the men, the days they work, an(J the hours per day 
are the causes, and the rods dug are the effects. The miss- 
ing term is the second effect. 

Solution. — 



.y = 4 X 9 = 3G days. 



c, 


a 


x^ 


n 4 


u 


i^ 


n 


9 


E^ 


E, 


X 


^9 



EVOIiUTION. 
83, Methods of Teaching Evolution.— -There are four 
methods of presenting this subject to pupils : 

1. To teach the process without giving reasons. 

2. To illustrate the process by means of geometrical 
figures. 

3. To illustrate by means of developed binomials or by 
formulas. See Evolution in the arithmetic published by the 
International Correspondence Schools. 

4. To employ both geometrical diagrams and developed 
binomials. 

Which of these is best it is perhaps not easy to decide. 
But the age and proficiency of the pupils should be considered. 
Our authors have exhausted their skill in presenting evolution 
so that it may be brought to the level of easy comprehension ; 
but every teacher, after finishing it with a class, has the 
feeling that it is seen "as through a glass, darkly." With 
the process itself there is little more difficulty than in long 
division, but it is otherwise with the reasons for the process. 
This naturally starts the question whether there are not many 



§ 2 PEDAGOGICS OF ARITHMETIC. 99 

subjects that should at first be taught only so far as the oper- 
ation is concerned, and the effort to reach a comprehension 
of the reasons therefor be deferred until greater compass of 
mind has been attained by the learner. A little reflection 
will convince the teacher that there are many such subjects. 
Grammar is full of them. The logic of cause and effect in 
history is utterly beyond the average intelligence of children 
in their first work in that subject. Yet we teach both early 
in the school work. 

Truths beyond us at first lie in the mind, and by the proc- 
ess known in pedagogy as apperception, they take their 
places later in classes to which at first they were not known 
to belong. The writer remembers that many years ago he 
learned and quoted, perhaps many hundreds of times, very 
glibly, " The subject of o. finite verbis put in the nominative 
case. " The word ' ' finite " had then no meaning to him. What 
" finite " has to do with verbs never started an inquiry in his 
mind. Afterward, while studying Latin, he learned that ' ' The 
subject of the infinitive is in the accusative " (objective). 
Then, by the apperceptive process, the words _/?;/ //rand infin- 
itive, with much accompanying knowledge of the subject, 
became parts of an organized whole, and in proper relation. 

Every one agrees that it is a good thing to have children 
memorize poetry, even if it contains thoughts and words they 
do not understand. A poem ripens as it lies in the mind, and, 
years afterwards, is perfectly understood, and may be a source 
of inspiration in the affairs of life, and an element in aesthetic 
culture. It appears, then, that it is often good pedagogy to 
teach processes only, even if the pupil is left to his own 
resources to get possession of the reasons afterward. 

With pupils of considerable maturity of mind, the explana- 
tion of evolution by means of the development of a binomial 
is undoubtedly the best. The second term of each power 
gives the trial divisor, and the terms that follow enable him 
to complete the divisor. Moreover, it is no longer necessary 
to remember the rule — only to write out the development of 
the binomial to a power equal to the index of the root. A 
very slight knowledge of algebra makes this an easy matter. 



b.tr<" 



100 



PEDAGOGICS OF ARITHMETIC. 



2 



The only powers of practical importance are two, the second 
power and the third power. 

To show the use of these developments, the extraction of the 
square root and of the cube root by this method is shown below. 

84. Square Root. — Suppose that the pupil has forgotten 
the rule. Square the binomial / -|" ^^ ^^ which / denotes tens 
and 7/ units. 

{f + ny = /' + Itu + le - f-^ (2/ + u)u. 

Example. — Find the square root of 7,569. 
Solution. — power root 

P + (3/ + u)u ■=. 7 5'6 9 I 80 + 7 = 87 

f = 640 

(2/+?^// = 

2/ = 1 6 



2/+U = 1 6 



1169 



1169 = {2/+7e)u. 



Explanation. — The greatest square (/") in the left-hand 
period is 6,400, and its square root (f) is 80. Taking this 
square from the power, there rem.ains 1,109, which is 
{'Zt-\- 7()i(. Of this product we know 2/, or 100, which is the 
greater part of one of the two factors. Dividing by 160 (2/) 
gives 7 for //. We now add 7 (//) to 100, and the result, 167, 
is 2t -\- H. Multiplying 167 by 7 gives the value of {2t -\- 7i)?{. 
If there were more figures in the root, we should have to 
regard those so far found as if they were one figure repre- 
senting units, and proceed as before. 

85. Cube Root. — We shall give somewhat more briefly 
an example in cube root, omitting imnecessary ciphers. 

Example. — E.xtract the cube root of 405,224. 



Solution. — 

P = 

{Zt- + ZtH + ir)H = 

3/^ = 14 7 

^ttt = 8 4 

iP ■= 16 



power root 
4 5'2 2 4 I 74 
843 



3/2 ^ ^f^^ _^j^-. _ 15 5 5 6 



62224 



2 2 2 4 = (S/"" + Ztu + uyt. 



2 



PEDAGOGICS OF ARITHMETIC. 



101 



86. The Foiirtli Koot. — The fourth root is, of course, 
found by extracting the square root of the square root; but, 
to illustrate the above method more fully, let us suppose that 
it is necessary to do this by one operation, as in cube root. 

(/ + uy = /' + 4/'// + Qt^u'' + 4.tu' + It' = /' + (4/' + Vyfu 
+ 4/;r + //')//. 

Example. — Extract the fourth root of 1,500,625. 

Solution. — power root 

fi + (4/3 ^_ f^f^i, + 4^fir- + u'')H - 1 5 O'O 6 3 5 1_35 

t' =81 

4P = 108 000 

Gf'u = 2 7 000 

A/u' = 3 00 

u^ = 12 5 



4r + 6/-U + 4//r + «' =: 13 8 12 5 



6 9 6 2 5 



6 9 6 2 5 = {4P+G/-u+4/u^+uye. 



87. Roots of Fractions. — Finding the square root of a 
fraction is easier if the fraction be first changed to an equiv- 
alent fraction having a perfect square for its denominator. 
Thus, 

" X"3 
3X3 



l/l = l/i^a = t/h|/5xc = j^. 



Vl = f1^5 = l4x= = iv^. 



This reduction may be taught to a class without any diffi- 
culty. It enables us to avoid extracting two roots and per- 
forming an awkward operation in division. Besides, it gives 
a more accurate result. The same method is applicable in 
finding the cube root of a fraction. Thus, 



n-i^' 



3X9 



27 



X18 



L^18. 



Vl = ^l;^s = l/rrx3 = ,^a 



It is a good exercise to make these reductions, but per- 
haps it is better to change the fraction to a decimal, and 
then extract the required root of the decimal. 



103 PEDAGOGICS OF ARITHMETIC. § 2 

88. Geometrical Illustration of Square and Cube 
Roots. — The writer is satisfied, after many years' experience 
in the classroom, that it is beyond the ability of pupils, even 
of those whose intelligence is above the average, to read and 
understand these illustrations, however skilfully they may be 
presented. If the teacher is expert with the crayon, and 
constructs the illustrations piece by piece as the numerical 
work proceeds, some of the class may be able to follow, 
though even these will have but an imperfect comprehen- 
sion of the logical force of the demonstration, and, in a 
brief time, the whole matter will have so faded as to be 
valueless. 

89. Evolution by Factoring. — It is often necessaiy to 
extract the square or the cube root of the product of several 
factors. In such cases the factors may sometimes be rear- 
ranged so that we may find the required root by inspection. 

Example 1.— Extract the square root of 50 X '72 X 18 X 162. 
Solution. — We notice that each factor contains a perfect square. 
Hence, we may write them thus, 25 X 36 X 9 X 81 X 2 X 2 X 2 X 2. 
Whence, the square root is 5 X 6 X 3 X 9 X 4 = 3,240. 

Example 2.— Find the cube root of 24 X 45 X 200 X 448 X 49. 
Solution. — Recomposing the factors, 
24 = 8 X 3 
45 = 9 X 5 

200 = 25 X 8 

448 = 64X7 

49 = 49. 

Hence, the product equals 8 X 27 X 125 X 512 X 343. 
Whence, the cube root equals 2X3X5X8X7 = 1,680. 

By preparing a list of such exercises, the teacher can add 
much interest to the subject of evolution and secure good 
review work in factoring. The readiest method of so doing 
is to begin with the indicated product of several cubes or 
squares, and recompose them so as to conceal the perfect 
powers. 

90. Reduction of Radical Forms. — To reduce to sim- 
plest form indicated roots of quantities containing a factor 



§ 2 PEDAGOGICS OF ARITHMETIC. 103 

that is of the same degree as the root indicated, is another 
easy and interesting exercise. Thus, 



4/50 = |/35 X 3 = 5\/2. 

-fT93 = feTxa = 4^ 3. 

The exercise aids in giving the pupil a more exact and 
discriminating notion of the meaning of evolution. 

91. Equal Factoi* Method of Extraetinjj: Roots. — It 

is important that pupils should fully understand the points 
of likeness between evolution and division. Many persons 
that use both processes with ease are unaware of the fact 
that evolution is only a special case of division just as invo- 
lution is only a variety of multiplication. Few pupils learn 
of these likenesses at the time when they study arithmetic, 
and if they discover them at all, it is later in life and by the 
merest accident. This should not be, and it will never hap- 
pen when the teacher himself imderstands in all their rela- 
tions the subjects he teaches. The usual definitions of 
division and evolution do not suggest this analogy, but they 
might easily be so formulated as to do so. Thus, 

Division is thr process of finding one of fzco /actors of a 
number x^'Iieu tlieir product and the oti/er factor are given. 

Evolution is the process of finding one of tioo or more equal 
factors ivJiose product and the number of factors are given. 

Square root is the process of finding one of tivo equal fac- 
tors li'hose product is given. 

Cube root is the process of finding one of three equal fac- 
tors ijhose product is given. 

There are several methods of extracting roots. Perhaps 
the least useful of these methods are those usually given 
in the arithmetics. These shall be passed without further 
notice in this place and a method explained that the writer 
believes to be much better and more easily tmderstood than 
any of them. It has the additional advantage of bringing 
out very clearly the likeness between division and evolution. 
It is a method derived from Sir Isaac Newton's Method of 
Approximating the Roots of Higher Equations. 



10-i PEDAGOGICS OF ARITHMETIC. § 2 

Example 1. — Find the square root of 89, that is, one of its two equal 
factors. 

Solution. — We begin by finding two numbers as nearly equal as 
possible whose product is 89 or nearly so. The numbers 9 and 10 will 
immediately suggest themselves, since 9 X 10 is 90- The true square 
root lies between 9 and 10; hence, we take their arithmetical mean, 
that is, half their sum, as being probably more nearly correct than 
either 9 or 10. 

Taking arithmetical mean, 

(9 +10) -^3 = 9.5. 

Now, assuming that 89 is the product of two equal factors, one of 
which is 9.5, we may find the other by division. 
Dividing, 

89-f-9.5 = 9. 868. 

We find that the factors 9.5 and 9.368 are not equal, but they are 
more nearly so than 9 and 10. It is evident that by taking the mean of 
9.4 and 9.368 and repeating the process, we shall obtain two factors 
still more nearly equal. 
Taking mean, 

(9. 5 + 9. 368) H- 3 = 9.434. 
Dividing, 

89 H- 9.434 = 9.4339633. 
Taking mean, 

(9.434+ 9.4339623) H- 3 = 9.4339811. 

This is the correct square root of 89 as far as it is carried. 

E.xAMiM.K 3. — Find the approximate square root of 1,971.14. 

Solution. — A brief inspection would suggest the two factors 50 and 
40, since 50 X 40 is 3,000. The mean of these factors is 45, which is too 
great, since 45 X 45 = 2,035. Hence, we may begin with 44 as the first 
mean. 

Dividing (using at first only 1,971), 

1,971-4-44 = 44.8, nearly. 

Taking mean, (44 + 44.8)^-3 = 44.4. 

Dividing, 1,971.14 -- 44.4 =44.395. 

Taking mean, (44. 4 + '14. 395) -- 3 = 44.3975. 

Dividing, 1,971.14 -- 44.8975 = 44.3975449. 

Taking mean, (44.3975 + 44.3975449) -- 3 = 44.39753245. 

The exact root corresponds with this to the last figure. Of 
course, the work is rarely carried so far. The preceding 
mean is correct to four decimal places, which is quite suffi- 
cient for ordinary calculations. The important points to be 
noted in this method are that sets of factors are successively 



§ 2 PEDAGOGICS OF ARITHMETIC. 105 

obtained that are more nearly equal than preceding sets, and 
that, finally, a set is found in which the factors differ so 
slightly that their mean may be taken as the required root. 

Example o. — Find the cube root of 937. 

Solution. — Here we must begin with three factors. Of course, the 
more nearly equal they are and the more closely their product 
approaches 937, the more rapidly we shall approximate the correct 
cube root. A brief inspection leads to the choice of the factors 
9.5, 10, and 10, whose continued product is 950. 

Taking mean, (9.5 + 10 + 10) -- 3 = 9.8, nearly. 

Dividing, 937 -f- 9.8 = 95.6123; 95.6132 -9.8 = 9.756. 

Taking mean, (9.8 + 9.8 + 9.756) -- 3 = 9.7853, nearly. 

This result is correct as far as three decimals ; but let us note the 
effect of repeating the operation. 

Dividing, 937 -f- (9.7853)- = 9.785686563. 

Taking mean, (9.7853 + 9.7853 + 9.785686563) h- 3 = 9.785438854. 

The cube root of 937 to seven decimal places is 9.7854388. 

Example 4. — Find the cube root of 61,331. 

Solution. — A brief inspection shows that the true result is between 
39 and 40. Taking the factors 39, 39.5, and 40, the mean of which is 
39.5, we proceed to find a new set of factors. 

Dividing, 61,331 -- (39.5)" = 39.303. 

Taking mean, (39.5 + 39.5 + 39.303) -- 3 = 39.434. 

This result is the correct root to three decimal places. 

Example 5. — Find the fourth root of 1,000. 

Solution. — The fourth root of a number is best found by taking the 
square root of its square root ; bt:t the object here is to show the process 
of equalizing four factors of 1,000. We may separate 1,000 into two 
nearly equal factors, 31^ and 33. Each of these is then separated into 
two factors as nearly equal as possible, 5 and 6|^, 5 and 6.4. 

Taking mean, (5 + 6.35 + 5 + 6.4) -f- 4 = 5.66, nearly. 

Dividing, 1,000-^(5.66)^ = 5.515066, nearly. 

Taking mean, (5.66 + 5.66 + 5.66 + 5.515066) -f- 4 = 5.63376+. 

The correct root to four decimal places is 5.6334. 

In finding the first factors it is a great advantage that they 
shall be as nearly equal as possible; for the more nearly 
they approximate the true root, the greater will be the num- 
ber of correct decimal places in each successive approxima- 
tion. To show this an example will now be solved in which, 
{a) TJie factors are nearly equal ; {b) The factors differ 
considerably. 



10(j PEDAGOGICS OF ARITHMETIC. § 3 

Example 6. — Find the cube root of 62. 

Solution. — (a) It is evident that the true root is very nearly 4. Taking 
4 and 4 as two of the three factors, the third is obtained by dividing, 

62 --(4X4) = 3.875. 

Finding mean, (4 + 4 + 3.875) -^ 3 = 3.958+. 

Dividing, 62 -i- (3.958+)- = 3.957675-. 

Finding mean, (3. 958 + 3. 958 + 8. 957675) h- 3 = 3. 957891. This result, 
after only two adjustments of the factors with which the work began, 
agrees throughout with the true root. 

{/>) Since 2x6x5^ = 63, let us begin with these factors. 

Finding mean, (2 + 6 + 5. 16+) -f- 3 = 4.3+. 

Now, we know that the root is less than 4 ; hence, our work is not so 
far advanced as the point of starting in ia) above. But. for the sake of 
the illustration, let us proceed. 

Dividing, 62 h- (4.3)^ = 3.35+. 

Taking mean, (4.3 + 4.3 + 3.35) -r- 3 = 3.98+. 

Dividing, 62 -h (3.98)^ - 3.914. 

Taking mean, (3.98 + 3.98 + 3.914) -- 3 = 3.958. 

Here, the mean is exactly the same as the first mean in {a). It is 
clear, then, that much labor is saved by care in the choice of factors. 

93. Finding? Factors Approximately Equal. — A 

little practice should make the pupil expert in separating any 
number into a set of factors that are nearly equal. The fol- 
lowing, however, will be found helpful: 

Example 1. — Separate 11 into two nearly equal factors. 

SuLUiiON. — We begin with 3 and 4, the mean of which is 3.5. But 
since 3.5 X 3.5 is 12.25, it is evident that 3.5 is considerably too great. 
We take 3.3, and dividing 11 by it, obtain 3.3333+ for the other factor. 
These two factors are so nearly equal that their mean is the square 
root of 11 correct to four decimal places. 

Example 2. — Separate 11 into a set of three nearly equal factors; 
also into a set of four such factors. 

Solution.— Since 2X2X2 = 8, and 2.4x2.4x2.4 = 13.824, it is 
clear that the factors desired lie between 2 and 2.4. Let us try 2.2. 
Dividing 11 by (2.2)^ we obtain 2.27+. Hence, 11 = 2.2 X 2.2 X 2.27, 
nearly. 

To find four such factors we may first find two factors of 11 as nearly 
equal as possible, and then separate each of these factors into two 
others. We know from example 1 that 3.3x3.33 = 11, very nearly. 
If now 3. 30 and 3.33 be each separated into two factors nearly equal, the 
problem is solved. Since 3.3 is less than 2 X 2 we know that the first 



§ 2 PEDAGOGICS OF ARITHMETIC. 107 

pair of factors are slightly less than 2. Now, since 1.8 X 1-8 = 3.24, we 
shall not be much astray if we take 3.3 = 1.8 X 1-84. In a similar 
way we inspect 3.33 and find it exactly equal to 1.8 X 1-85. Hence, our 
four factors are 1.8, 1.84, 1.8, and 1.85, and their mean is 1.8225—, very 
nearly the fourth root of 11. 

Example 3. — Find five factors, nearly equal, of 3,827,963. 

Solution. — -Pointing this number into periods, as in finding the fifth 
root, 38'27963, we see that the required factors must have two integral 
places. Since 20' = 3,200,000 and 2P = 4,084,101, it is evident that 
the required factors are not much different from 20.7. Dividing, 
therefore, by 20. 7^ we obtain the fifth factor, 20.85, nearly. Hence, 
3,827,963 = 20.7^ X 20.85. 

Example 4. — Separate .0823 into three approximately equal factors. 

Solution. — Dividing .0823 into periods as if for finding the cube 
root, we have .082'300. This may be for the time regarded as a whole 
number 82,300; of this the cube root is between 40 and 45, say 43. 
Dividing 82,300 by 43^ we obtain 44.51, nearly. Hence, 82,300 
= 43- X 44.51. Returning now to the consideration of the decimal 
point, we see that .0823 = .43'^ X -4451. 



EXAMPLES FOR PRACTICE. 

93. Solve the following: 

1. Separate each of these numbers into two nearly equal factors 
and find the mean of each pair: (a) 187; (i) 2,449; (r)7; (--O-^l; {^')-085. 

2. Separate each of the following numbers into three factors, as 
above: ((?)700: (/;) .0715; (r) 387,496; (r/).0067; 0') 50.07. 

3. In finding the square root of 4,137, if 64.2 is chosen as the first 

factor, what is the other, and what is the first mean? 

64.44+. 

64.32. 

4. Use 7.1 and 7.25 as two of the factors in finding the cube root of 
376, and then find the other and their mean. 

A 5 ''•^+- 

Ans. I ^ 2^,__ 

5. By the foregoing method find the following correct to four deci- 
mal places: 



Ans. I 



{a) i/i;079; {d) ^1,428; (<;) ^1,541; (^/) ^559; (c) -^^3,000. 

' (a) 32.8481. 
{l>) 11.2609. 
Ans.<! (c) 11.5505. 

(d) 8.23766. 

(e) 4.9592. 



108 PEDAGOGICS OF ARITHMETIC. § 2 

94. Dr. Brooks' Method of Extracting Cvibe Root. 

In his " Philosophy of Arithmetic," Dr. Brooks gives a very 
good method for finding the cube root of numbers. In intro- 
ducing it he says : "I will now present a method of extract- 
ing cube root that is much simpler and more convenient 
than the ordinary one, and, indeed, than any other with 
which I am acquainted. This method seems to have been 
approximated by several writers, although I have not found 
any that presents it in the form in which it is here given." 

Example 1.— Extract the cube root of 14,706,125. 
Solution. — 



(a) 


(^) 


('■) 


2 


1 2 tr. 


1 4'7 6'1 2 5 1 2 4 5 


4 
64 


r 256 

- 14 5 6 com. 


8 
^6706 


8 


1 6 


(5824 


725 


1 7 2 8 tr. 

C625 
17 6 4 2 5 com. 


r8821 25 
[882 125 



Explanation. — Write the first root figure 2 at the top of 
column (a), 3 times its square with two ciphers annexed at 
the top of column (d), and its cube, 8, under the left-hand 
period of column (r). Subtract the cube from the period 
above it and annex to the remainder the next period. Divide 
6,706 by 1,200, regarded as a trial divisor that is to be 
increased. The quotient 4 is written as the next root figure. 
Add twice the first root figure to the number in column (a), 
and to the sum annex the second root figure, thus obtaining 
64; multiply this by the second root figure and write the 
product imder the trial divisor in (d) ; multiply their sum, 
1,456, by the second root figure, subtract the product, 5,824, 
from 6,706, and to the remainder annex the next period for a 
new dividend. 

Now add the square of 4, the second figure of the root, 
1,456, and 256 and use their sum with two ciphers annexed, 
172,800, as a new trial divisor. Divide by the trial divisor 
and write the quotient" 5 as the third root figure. To 64 in 
column (a) add twice the second root figure, and to the sum 



§ 2 PEDAGOGICS OF ARITHMETIC. 109 

annex the third root figure, thus obtaining 725. Multiply 
725 by the third root figure, and add the product o,(;i25 to 
the second trial divisor in column (//). Multiply the com- 
plete divisor thus obtained by the third root figure, write 
the product under the last dividend in column (r), and sub- 
tract. There being no remainder, the root is exact. 



DR. BROOKS' RULE. 

I. Separate the mnnber into periods of three figures eaeh; 
find the greatest iiuiuber whose eube is contained in the left- 
hand period, and write it in the root. 

II. Write the first term of t lie root at the top of eolnnin {cx), 
three times its square, %vith two annexed eiphers at the top of 
column (/?), and its cube under the first period; subtract, 
and annex the next period to tlie remainder for a dividend ; 
divide by the last number in column [b) as a trial divisor, and 
write the quotient as the secojid figure of the root. 

III. Add twice the first figure of the root to the number 
in column {a) ; annex the second figure of the root, multiply 
the result by the second figure of the root ajid add the product 
to the trial divisor to form the complete divisor. Multiply 
the complete divisor by the last root figure, subtract the prod- 
uct from the dividend, and to the remainder annex the next 
period for a nciv dividend. 

IV. Square the last figure of the root, take the sum of this 
square, the last complete divisor and the number next above 
it in column (/;), and annex to this sum two ciphers to forma 
nezu trial divisor; divide the dividend by this trial divisor 
for the next root figure. 

Y. Add tioice the second figure of the root to the last 
number in column {a) ; to this sum annex the last root figure, 
multiply the result by the last root figure, and add the result 
to the trial divisor for a complete divisor. Use this complete 
divisor as be/ore, and thus continue until all the periods have 
been used. 



110 PEDAGOGICS OF ARITHMETIC. § 2 

Example 2. — Extract by the foregoing rule the cube root of 
41,673,648,563. 
Solution.^ 
(a) (/;) (c) 

3 2 7 tr. 4 1'6 7 3'6 4 8'5 6 3 | 3467 

6 f 376 27 



9 4 ^3076 com. i 14673 

8 16 112304 



3 4 6 8 tr. 
6 156 



1038 7 -; 3 52956 com. 
[ 3_6 



35914800 tr. 

72 709 
35987509 com. 




MENSURATION. 

95. Formulas In Meustiration. — The Committee of 
Fifteen in its report urges that pupils, in connection with 
their work in arithmetic, should be taught the use of 
the equation. By this is meant the simple equation 
with one or more unknowns, and the quadratic equation 
with rational roots. A very slight knowledge of the 
equation will enable the pupil to derive from fundamental 
formulas other formulas covering all the cases relating 
to the circle, sphere, etc. Without this ability, he must 
remember arbitrary rules containing many different deci- 
mal forms; with it, he remembers only a very few funda- 
mental formulas, and as occasion arises, he derives in a 
moment the formula required. Moreover, he is able to 
derive the decimal he should find in his textbook; or, 
better still, he can avoid the use of all decimals except 
that denoted by the Greek letter - (pronounced//), 3.1416. 
To show this, we shall take the cases of the circle and the 
sphere. 

96. The Circle. — Designate by D the diameter, by R 
the radius, by C the circumference, by A the area, and 



§ 2 PEDAGOGICS OF ARITHMETIC. Ill 

by -, o.lllG. The fundamental formulas that the pupil must 
remember are : 





C 


= - D, or 2 - A', 


(1) 


and 


A 


= - R\ or i - D\ 


(3) 


From (1), 




D = ^, 


(3) 


and 




-^• 


(4) 


From (2) 






(5) 


and 




D = 2./d.. 


(C) 



c 

By substituting — for R in (5), and finding A from the 
resulting equation, 

and C = 2V^^. (8) 

The foregoing give each element of the circle in terms of 
any other. An interesting exercise consists in changing 
these formulas into the rules found in the textbooks. 

Thus, (:5) = D = \xC = .3183 C. 

The student will see that the decimal .3183 is the recipro- 
cal of -; that is, it is l-f-3.141G, The derived rule should 
read : 

To Find tlie Diameter of a Circle Avlien tlie Cireiim- 
fereiiee is Given. — Multiply tJic circuviferoicc by the con- 
stant .S18S. 

Hence, (4) z= A = -1-x C = .15915 C. 
Again, (7) = ^ = ^ = -IxC^ = .70577 (^^ 

This converted into the language of an ordinary rule is: 
To Find tlie Area Avlien the Cii'ciiniferenee is Given. 

Multiply the square of the circumference by .79577. 



112 PEDAGOGICS OF ARITHMETIC. § 3 

97. The Spliere. — -The surface of a sphere may be 
denoted by S, its volume by V, and its other elements as in 
the circle. The formulas from which all others are derived 
are: 





5 = 


- n\ or 4 - R\ 


(1) 


and 


V = 


ir:I)\ or ir:R\ 


(2) 


From (1), 




D^ /I 


(3) 


and 




R = ./I 


(4) 


From (2), 




n^i/-\ 


(5) 


and 




- = n- 


(6) 


Since D = 


— , and 


R ^- [^_, if we 


substit- 


in the formul, 


as above 


; and reduce, we 


: have 


from (1), 






(-) 


and 




C = Vr:S. 


(8) 


From (2), 




V — 


(^) 


and 


C = #(;;r^F. 


(10) 



As in the case of the circle, the pupils should be required 
to convert the formulas into rules. They should also answer 
such questions as, If tJic diameter is g'iveii, ivhich formn/a 
will give the surface ? Another good exercise, either for 
home work or classroom work, is to make examples answer- 
ing to certain formulas. 

Of course, the fundamental formulas are those most gen- 
erally used, and are all that are commonly given. The 
derivations shown above, however, are important for the 
reasons that they generalize the subject, and fvirnish excel- 
lent discipline. 



§ 2 PEDAGOGICS OF ARITHMETIC. 113 

98. Application to Other ^lagnitudes. — The formulas 
of the circle apply equally well to the cylinder, the cone, 
and its frustum, when the element 77, representing the alti- 
tude, is introduced. This the teacher will find entirely easy 
and instructive. 



MISCELLANEOUS. 

99. Leap Years. — Very few persons understand the 
reason for leap years, or the explanation relative to them. 
Since this explanation furnishes a specimen of analysis dif- 
ferent from any found elsewhere in the arithmetical course, 
it is given here. 

The calendar established by Julius Caesar had three years 
of 365 days each, followed by one of 300 days — an average 
of 365 days 6 hours. By the year 1582, this method had lost 
10 days. Pope Gregory then ordained that October 5 should 
be October 15, and that centennial years, as 1700, 1800, etc., 
should be common years, unless they were multiples of 100, 
as 1600, 2000, etc. This calendar is now in general use in 
Christian countries. Russia, however, has hitherto adhered 
to the Julian calendar, which is now 13 days behind the 
Gregorian calendar; but that countr}^ has decided to abandon 
the Old Style calendar and to adopt the Gregorian calendar. 

Analysis. — True year = 305 da. 5 h. 48 m. 49.7 sec. 
Calling 305 da. a year, we lose each year 5 h. 48 m. 40.7 sec. 

In 4 years we lose 4 times this, or 23 h. 15 m. 18.8 sec. 
Calling the 4th year 306 days, we £'di/i 24 h.— (23 h. 15 m. 
18.8 sec.) = 44 m. 41.2 sec. 

In 100 years we gain 25 times this, or 18 h. 37 m. 10 sec. 
Calling the 100th year 365 days, we /ose 24 h.- (18 h. 37 m. 
10 sec.) = 5 h. 22 m. 50 sec. 

In 400 years we lose 4 times this, or 21 h. 31 m. 20 sec. 
Calling the 400th year 366 days, \\q gain 24 h.— (21 h. 31 m. 
20 sec.) = 2 h. 28 m. 40 sec. 

In 4,000 years the gain is 10 times this, or 24 h. 40 m. 
40 sec. By not calling the 4,000th year 300 days, we are 
ahead only 46 m. 40 sec. 



114 PEDAGOGICS OF ARITHMETIC. § 2 

By thus continuing to count each 4,000th year as a com- 
mon year, it will take 123,429 years to gain one day. We 
may safely assume that the correction for each 4,000th year 
will be made at the proper time. 

It would be a curious calculation to count how far a nation 
that adheres to the Julian calendar will be behind by the 
end of the time given above — 123,429 years. 

100. Riglit-Angled Triangles. — Every teacher that 
has undertaken to make a class familiar with the properties 
of the right-angled triangle has felt the need of having sotne 
method of finding numbers so related that the square of one 
shall be equal to the sum of the squares of two others. The 
numbers 3, 4, and 5, and equimultiples of them are well 
known to be such, but are there any others ? This matter 
has engaged the attention of mathematicians for centuries, 
with the result that we have many celebrated rules for find- 
ing such numbers. Among them are : 

Pythagoras'' Rule. — Let ;/ = any odd number; then will 

ie-\ , ;/= + 1 ^ , 

— - — • and — - — be the other two numbers. 

ii" — 1 ;/' + 1 

Thus, let ;/ =z 7; then — ~— = 24, and — ^— = 25; and 

24^ + 7' = 25^ 

Plato s Rule. — Let )i = any even number; then -t""-^ ^^^ 

u" 

—- -|- 1 will be the other two numbers. 

•i 

Thus, let // = 10; then ^ — 1 = 24, and ^ + 1 = 2G; and 

4 4 

10^ + 24^ = 2{]\ 

Euclid's Rule. — Let x and j' be any numbers both odd or 
both even, such that their product is a perfect square. 

X — y X •\- y 

Then the numbers are \ x y, ' — — =-, and 



2 ' 2 

Thus, let X = 27 and y = 3 ; then VTj' = 9, '^^^' = 12, 

and ^-^^ = 15; and 9^ + 12"' = 151 



§ 3 PEDAGOGICS OF ARITHMETIC. 115 

But the following- method, used by the writer, will per- 
haps be most useful in practice: 

Take any fraction and its reciprocal. 
The three numbers will be — 

1. Twice the product of the denominators. 

2. The sum of the cross products. 

.3. The difference of the cross products. 

Thus, take | and f. 

1. z= 5 X 3 X 2 = 30 ] 15 ] 

2. = 25 + = 34 y, or 17 |^. And 15^ + 8^ = 17^ 

3. = 25-1) = IG J 8 J 

101. Aritlinietical Progression. — Our works on arith- 
metic usually contain a table of formulas all derived from 
the fundamental formulas relating to this subject. For the 
pupil having a rudimentary knowledge of algebra, such as 
the Committee of Fifteen recommends for the upper gram- 
mar grades, there is no more interesting exercise than the 
derivation of this table. This work should be done, not for 
the sake of the formulas, but for the discipline it involves. 

The formulas from which those of the table are obtained 
are: 

5 = fc±^ (1), and / = ai-{u- l)d. (2) 

102. The Metric System. — While in this country the 
use of the metric system has not been introduced into ordi- 
nary commercial transactions, and perhaps never will be, its 
use in science has become quite general. It is therefore 
important that the teacher should be familiar with its most 
generally used unitg. An advanced course in arithmetic 
should include this system, but it should be taught in a 
practical manner. The classroom should be furnished with 
measures of the meter and the liter, and with weights of the 
gram and the kilogram. The pupil should be required to 
use them imtil he can think in these units of weights and 
distances without the necessity of translating them into their 
equivalents in our measures. When this degree of proficiency 



IIG PEDAGOGICS OF ARITHMETIC. §2 

has been reached, and not before, he should be made familiar 
with the numerical relations between them and the units that 
we employ. The classroom and its furniture, together with 
doors and windows, should be measured with the meter, and 
their dimensions written in meters and decimals of a meter. 
Areas and volumes should be calculated, and the pupil be 
made thoroughly to understand how^ to manipulate the deci- 
mal point in tlie redtiction of magnitudes of one, two, and 
three dimensions. Water, grain, etc. shoiild be measured in 
liters, and articles weighed in grams and kilograms. Pre- 
liminary to measuring and weighing, estimates should be 
required of the pupil. By this means the rivalry of conjec- 
ture is introduced and the interest much enhanced. 

It was recommended above that the translation of metric 
measures into their English equivalents should be deferred 
to the last. The reason is obvious. No student of German 
is proficient until he can ililiik in that language, without 
thinking of the equivalent in his own tongue. 

It is a pity that so excellent a system should not be tmiver- 
sally used, and that the people of this country have not 
accepted its legalization by Congress. Every civilized nation 
in the world, except Russia and Montenegro, has legalized 
it, and in most of the countries where it has been legalized 
it is in general use. The international standard meter and 
kilogram were received by this country in 1800 from the 
International Committee, and they are now in the custody of 
the office of Standard Weights and Measures, at Washington. 
They are made of platinum-iridium, 10^ being iridium. 
The original is a metallic rod, on which are two lines one 
meter apart. It is preserved at Paris among the archives 
of the International Metric Commission. 

103. The Meter. — All the units of the metric system 
are derived directly from the meter. This was obtained by 
measuring with extreme care the distance from Barcelona, in 
Spain, to Dunkirk, in France, and from the arc thus obtained, 
calculating the distance from the equator to the poles. One 
ten-millionth of this distance was taken as the standard, 



§ 2 PEDAGOGICS OF ARITHMETIC. 117 

equal to 30.37+ inches. It was afterward found, however, 
that the true length of a meter is slightly less than that 
determined by the first calculations. Notwithstanding the 
error, the length as first found was retained, it being imma- 
terial whether the length of the standard meter be one ten- 
millionth of the distance from the equator to the poles or 
not, so long as the standard bar is not lost or destroyed. 

From the meter, by multiplication and division, all the 
other units of the system are obtained. Multiples are denoted 
by Greek prefixes, and submultiples by Latin prefixes; 

Thus, 1 decameter (Dm.) = 10 meters (m). 
1 decimeter (dm.) = yL meter. 
1 hectoliter (HI.) = lOO liters (1). 
1 centiliter (cl.) = jlj^ liter. 

The iinits of length for very short distances are the milli- 
meter and the centimeter, for moderate distances the meter, 
and for greater distances the kilometer. 

Surface tmits are the square centimeter and the square 
meter. In measuring land, the square meter is called a 
centare; 100 centares make 1 are, and 100 ares a hectare. 

Volume imits are the cubic centimeter and the cubic 
meter. In measuring wood and stone, the cubic meter is 
called a stere. 

The units of capacity measure, corresponding to our dry 
and liquid measure, are derived from the liter, which is the 
volume of 1 cubic decimeter. The principal units are the 
centiliter, the liter, and the hectoliter. 

For measures of weight, the gram, equal to the weight of 
1 cubic centimeter of distilled water at its greatest density 
(39.4°), is taken as the standard. The principal units are the 
centigram, the gram, the kilogram, and the tonneau. 

It is worth noting that ovir 5-cent coin, called the nickel, 
weighs 5 grams, and is 2 centimeters in diameter. 



PEDAGOGICS OF GRAMMAR, 

(PART 1.) 



INTRODUCTION. 



GE:N^EriAL REMARKS. 

1 . Defluitioii of Eangiiag-e. — As is the case with most 
subjects, even the simplest, there is great diversity in the 
definitions of language and grammar. Goold Brown says, 
"" Ijanjyiiage, in its primitive sense, embraced only vocal 
expression, or human speech uttered by the mouth ; but after 
letters were invented to represent articulate sounds, language 
became twofold, spoken and i^'rittcii ; so that the term lan- 
guage now signifies, any scries of sounds or letters forvicd 
into words and employed for the expression of thoicght." 

Another author, Sheridan, scarcely less celebrated than the 
authority quoted above, remarks: " The first thought that 
would occur to any one that had not properly considered the 
point, is, that language is composed of words. And yet this is 
so far from being an adequate idea of language, that the point 
in which most men think its very essence to consist, is not even 
a necessary property of language. For language, in its full 
extent, is any way or method whatsoever by which all that 
passes in the mind of one man may be manifested to another. " 

This definition includes the deaf and dumb language, 
together with that of the blind, and the gestures and facial 
expressions employed in ordinary speech and oratory. 

S 3 



2 PEDAGOGICS OF GRAMMAR. § 3 

Professor Whitney, in his " Life and Growth of Language," 
makes the scope of the definition of language as comprehensive 
as the foregoing. ' ' Language, then, " he says, ' ' sign-ifies cer- 
tain instrumentaHties whereby men consciously and with inten- 
tion represent their thought, to the end, chiefly, of making it 
known to other men : it is expression for the sake of communi- 
cation. The instrumentalities capable of being used for this 
purpose, and actually more or less used, are various: gesture 
and grimace, pictorial or written signs, and uttered or spoken 
signs ; the first two addressed to the eye, the last to the ear. " 

For what is contemplated in this work, the meaning of the 
term may be restricted as follows: 

Tjanguage is the body of uttered or tor it ten signs employed 
by men inconniiunieating tJiouglit. This restricted definition 
is necessary, because the teaching of language, in our ordi- 
nary schools, deals only with written or printed matter, and 
with thought expressed orally To indicate in outline how 
language may bs taught so that piipils may employ it more 
effectively in the expression of their thought is, in these 
pages, the primary object. Many, indeed most, teachers, 
while they may possess a more or less complete knowledge 
of the language they teach, — its gratnmar and rhetoric, — 
need much technical and professional instruction in the art 
they practice. While much has been written, and well writ- 
ten, on language teaching, and on grammar, it has been 
mostly in the form of textbooks for the use of pupils. 
Thoughtful and progressive teachers have doubtless been 
able to glean from these books many helpful devices and 
suggestions of improved methods of procedure. No attempt, 
however worthy of mention, has been made to present in a 
body the hints, principles, and methods constituting what 
may be called The Pedagogics of Language and Grammar. 
Such is the purpose of this work ; to furnish, as nearly as may 
be, such help as an intelligent supervisor of the work of a 
large body of teachers should wish to render. 

3. Defluition of Graniiiiai*. — In. a scientific treatment 
of any subject, the first requisite is a definition of the matter 



§ 3 PEDAGOGICS OF GRAMMAR. 3 

under discussion. But if it be true, as has been asserted, 
that English is a " grrammarless tongue," we are confronted 
with the difficulty of defining that which has no existence. 
An attempt to define English grammar was made before the 
time of Shakespeare. It was as follows: 

''EnjiiisU g-ramniar is the art of speaking and writing 
the Engl is /i language eorreet/y." 

This definition, with occasional slight changes in the word- 
ing, has been acceptecl by grammatical writers ever since. 
" In accordance with established usage," " with propriety," 
or other equivalent phrase has displaced "correctly" in 
the definition. A little reflection will make it obvious 
that the definition, even when thus modified, is inadequate. 
"Correctly" and the other phrases imply an established 
standard of writing and speaking. But how, and by whom, 
was the standard instituted? Certainly not by the authors 
of ow: English classics, for no two of them agree. Are 
the dictionaries to be relied upon for this standard of pro- 
priety? Surely not, for tliey are not uniform in their spell- 
ing, syllabication, or pronunciation. In point of fact, there 
is no established standard of accuracy in the use of our 
language, and the definition is therefore inadequate. 

Professor ]\Iaetzner, probably the greatest of writers on 
English Grammar, says, "Grammar, or the doctrine of 
language, treats of the laws of speech, and in the first place, 
of the zvord, as its fundamental constituent with respect to 
its matter and \\.% form ; of prosody^ or of the doctrine of 
sounds, and of morphology^, or the doctrine of forms, and 
then of the eoudunation of v\'ords in speech; of syntax, or 
the doctrine of the foriuing of words and sentences." 

It is impossible to determine whether anything more than 
spoken language is included by the foregoing. The meaning 
depends upon what is meant by the word speeeh. Indeed, 
many eminent authorities insist that grammar has to do only 
with spoken language. 

Professor Whitney limits the domain of grammar to 
etymology or form, and syntax or construction, and many 
other writers agree with him in this. 



4 PEDAGOGICS OF GRAMMAR. § 3 

The difficulty of defining grammar has driven most late 
writers to take the old definition, or to omit a definition. In 
examination, students are very frequently required to define 
grammar; when such is the case, the old definition quoted 
above is always regarded by examiners as acceptable. 

3. Failure of Definition. — Any definition of grammar 
that does not truthfully describe its scope and the purpose 
and result of studying it, fails to conform to the test of a 
perfect definition. Now, it is certain, as the result of long 
observation and experience on the part of those called upon 
to teach the grammar of our "grammarless tongue," that 
the study of the subject as found in books constructed on the 
model of the Latin and the Greek grammars, has done little to 
improve the student in the ' ' art of speaking and writing the 
English language correctly. " This fact has slowly compelled 
the study of language to be turned to the sentence as the 
most important unit in language, and to the relations of its 
parts as the principal matter to be considered. It is not now 
a matter of dispute among educators whether the study of 
technical grammar, under its fourfold divisions of orthog- 
raphy, etymology, syntax, and prosody, with its flippant 
foolishness of parsing, and its reference to rules, has any 
practical value. "John is a noun, because it is a name; 
proper, because it is a particular name," and so on, soon 
degenerates into a mechanical exercise that excites no mental 
movement whatever. It in no way prepares the pupil for 
the active life awaiting him, by furnishing either useful 
knowledge or mental discipline. That he should know the 
etymology of his language is conceded, but not that he 
should acquire the knowledge by such mind-paralyzing 
methods. The phenomenon known among educators as 
"arrested development" soon results from such exercises. 

4. Value of Grammatical Study. — The principal 
benefits to be realized in pursuing any study are two : 

1. TJie acquirement of useful knoivledge. 

2. The gaining of mental discipline. 



§ 3 PEDAGOGICS OF GRAMMAR. 5 

Now, the study of grammar has value in the former 
respect; but, properly taught, there are few subjects so 
valuable for disciplining the mental faculties. Tyndall, in 
speaking of his early studies, tells of the delight and profit 
he found in disentangling the intricacies found in the con- 
struction of some of Milton's sentences. In such exercises, 
the main points are to discover the relations among the 
constituent parts of the sentence, and to determine questions 
of doubtful etymology. Every such operation of the mental 
faculties improves the judgment by appealing to the power 
of discrimination, sharpens the perceptions, and develops the 
reasoning power. 



TEXTBOOKS. 

5. The t/atest Textbooks. — After many years of trial 
of the grammars constructed on the models of the Greek and 
the Latin grammars, it came to pass that the conviction 
became general among teachers that the study of books so 
constructed is utterly useless, either for knowledge or dis- 
cipline. As is usual in such cases, the first swing of the 
pendulum of reform carried us far beyond the golden mean. 
The subject, as formerly taught, was abandoned utterly, 
and "Language Lessons" were substituted for grammar. 
The technical terms of etymology and syntax were displaced 
by such terms as "name words," " action words, " "how-when- 
and- where words," "link words," and so on. But so weary 
had teachers become of the old way of teaching grammar, that 
the new books were sold by hundreds of car loads. The 
revulsion came speedily. It was soon found that the last 
state of things was worse than the first, and many teachers 
returned to the former method. This they did the more 
easily from the fact that they were familiar with the 
machinery of the old — they knew, and could give glibly, by 
number, all the "observations," all the "rules," and all the 
" exceptions." 

Thoughtful educators gradually perceived that the old 
method, however bad it may be as a whole, contains many 



6 PEDAGOGICS OF GRAMMAR. § 3 

things necessary in the contemplated reform. Its etymology 
cannot be much improved upon, and its syntax, with certain 
prunings, additions, and readjustments, must be retained. 
It was perceived that noun and verb are better than name 
word and action %vord^ and so for most of the technical terms 
of etymology; that the sense and the sentence are the main 
considerations in language and grammar. 

It was found, too, if we would get to a middle ground, that 
in the earliest books issued under the regime of reform, there 
are many things that should be utilized. The analysis of the 
old should be combined with the synthesis of the new, and 
some of the practical matters proposed, such as composition, 
with letter writing and business forms, should not be ignored. 
But where there are " many men of many minds, " general 
convictions crystallize slowly; and it is only after twenty 
years of experiment and uncertainty that we begin to see 
works representing the best of both extremes. 

6. Manner of Educational Progress. — It may be 

remarked that the best of anything connected with human 
progress does not continue to be the best for any consider- 
able tiine, but changing conditions require modifications and 
readjustments. Progress in methods of procedure is simply 
a matter of evolution, and this is necessarily slow. The 
doctrine of "the .survival of the fittest " is conditioned by the 
fact that the fittest at any given time, if it is to continue to 
be the fittest, must be slowly modified and readapted. So 
that the brocard, "Of the making of books there is no end " 
may be written, "Of the making of textbooks there is no 
end." Our great publishing houses at much expense issue 
textbooks, only to follow them the next year by others sup- 
posed to be in some respects more nearly consonant with the 
needs of the teachers and pupils that use them. If, there- 
fore, any one were to assume to sketch with some detail the 
ideal grammar, it must be with the limitations indicated above. 
Moreover, the textbooks best adapted to the teachers and 
pupils of one part of a country, may not, by any means, be 
that best suited to the needs of those in another part of the 



§ 3 PEDAGOGICS OF GRAMMAR. 7 

country. It may be tirged, however, that if the textbook 
that has been found to be the best where progress in educa- 
tional methods is known to be greatest, be introduced else- 
where, the use of it establishes a tendency toward a more 
rapid and correct progress. 

7. Value of Textbooks and Metliods. — The character 
of the work done by a particular teacher is determined less 
by the pedagogical excellence of his method and the textbook 
he uses than is generally supposed. 

In the first place, a study may be introduced too early or 
too late. The different faculties are developed, not simul- 
taneously, but in a certain fixed order. If, for example, the 
most skilful teacher conceivable were to attempt to teach 
logic, grammar, ethics, or the higher mathematics to children 
in primary grades, he would inevitably fail, however excellent 
might be his textbooks. The subjects address themselves 
to the reasoning powers, and only after these powers have 
attained an advanced stage of development. The vocabulary 
of the pupil must be large, and he must be able to get along 
without the aid of the concrete and to deal with abstractions. 
It is true, however, that the most elementary concepts of 
grammar may be presented to 3'oimg pupils by means of 
abundant illustrations, and by the induction plan, and thereby 
may be laid a good foundation for the niore critical and diiTfi- 
cult work that must come later. It is, therefore, obvious 
that the grammar for beginners should be as elementary as 
possible. 

Again, even with the aid of an ideal textbook on grammar, 
failure to secure good results is not impossible — indeed it is 
very probable. Not every one can use the sword of Douglas 
or swing the club of Hercules. The teacher must have a 
mind that can discriminate keenly and reason accurately. 
Moreover, he must know his subject thoroughly, both in 
itself and in its relations and applications. The writer 
remembers a lecture by an eminent teacher, who related 
the incidents of a call he had received, late at night, from 
a young man anxious to learn the secret of the lecturer's 



8 PEDAGOGICS OF GRAMMAR. § 3 

success as a teacher. " I told him," said the lecturer, " down 
to the minutest details, my method of doing my work. He 
made careful notes of what I said, and seemed to understand 
me. He thanked me, and when about to go, expressed the 
belief that in time he should be able to employ my method 
successfully. I assured him that he would probably fail. To 
his surprised inquiries as to the reasons for my doubt of his 
success, I told him that no two persons can use the same 
method with equal success; that to the method is superadded 
something that belongs to the personality — an intangible, 
magnetic, indescribable something that reminds one of the 
overtones of different musical instruments; that no teacher, 
compelled to follow slavishly the methods prescribed by 
another, can possibly be at his best. Put your own person- 
ality into your work, and if you do not succeed, your case is 
hopeless. " 

8. What to Omit From a Textbook on Ijaiigxiage 
and Grammai*. — Strictly speaking", the study of the English 
language includes much more than has ever been embodied 
in a single work on the subject. Under the general division 
of orthography — including orthoepy — we have the various 
printed and written forms of the letters, with their sotmds, 
or phonics ; the combination of letters into words, and the 
meanings of the words so formed, together with the diacrit- 
ical and other accessory marks. 

Etymology classifies these words, the basis of classification 
being their function as employed in speech, together with 
their changes of form, or inflections. 

The syntax of the language treats of the combination of 
words into sentences, the various forms of sentences, the 
relation and government of their constituent parts, and the 
sense or meaning of sentences, at least so far as is necessary 
to determine the relation of their parts. The subjects of 
capitals and punctuation are also involved, as affecting the 
approved written forms of sentences. 

Here belongs also the subject of coin2>osition in its vari- 
ous forms of letter luriting, business forms, essays, etc. 



§ 3 PEDAGOGICS OF GRAMMAR. 9 

Involved not only with composition, but also with its con- 
stituent, the sentence, are arrangement, style, etc. — cover- 
ing the entire domain of rlietoric*. 

Prosody with its many varieties of feet and their combi- 
nations into the numerous forms of metrical compositions, 
belongs, at least partially, in the domain of syntax. Rhetoric, 
with its figures of speech that owe their existence to poetry, 
is indispensable io prosody. 

Eloeution, or " the art of correct intonation, inflection, and 
gesture in public speaking and reading," belongs also in 
language study. 

It might be shown that the scope of language study is 
much wider than is indicated above, but enough has been 
given to make it clear that to decide what should be omitted 
from a work on grammar is by no means easy. Still more 
difficult is it to determine what should be found in a work on 
grammar and language. The student may be convinced of 
the truth of these observations by examining a numl^er of the 
grammars issued during the last fifty years. 

While it is perhaps impossible to sa.y what sul^jccts should 
be omitted from a work of this kind, and very difficult to 
decide what it should contain, yet in this task we may wisely 
permit ourselves to be guided, in a general way, by eminent 
writers on language, such as Professors Bain, Whitney, and 
others of their class. We have, besides, examples of books 
lately written by educators that have evidently studied the 
matter carefully, and have practical acquaintance with the 
demands of the times and the needs of the classroom. 

0. AVliat a Textliook on Language and Grammar 
Sliotild Contain. — We may take, as a criterion of selection, 
Mr. Spencer's dictum that the end sought for in any study is 
twofold : 

1. Mental discipline. 

2. The acquirement of practical knowledge — knowledge 
that will be of use in gaining a livelihood. 

As an additional help, we shall perhaps not err in assuming 
the truth of what is urged by the authorities mentioned just 



10 PEDAGOGICS OF GRAMMAR. § 3 

above, that in g'ramniar the scnsi' and the sciitoicc are the 
main thing's to be considered. 

If these criteria be assumed, it follows, almost inevitably, 
what such a work should contain. If, besides, we find that 
the latest and most approved textbooks exemplify these 
requirements, we may be reasonably sure of our ground. 
Every matter proposed for admission t(^ a textbook must 
satisfactorily answer the test, qui bono? — what is it good 
for ? — or be rejected. 

Excluding the histo7-y and a)itiqnitics of the language, 
curious and interesting though they be, and orthography — 
the Ictlcr — with its vozvcls, its cojisonants, its phonics, from 
all of which we suffered in childhood, w^e come to etyniol- 
og-y — tlie Avoi'cl. The subject of etymology should be found 
in every rational work on grammar. That its treatment 
should occur first in the arrangement of topics does not fol- 
low, but stripped of all its curiosities of Saxon, French, 
Latin, and other derivations, its classifications should be 
made familiar to the pupil by all the available devices that 
have been proved to be valuable. By similar means, its 
inilections must be taught and emphasized by appropriate 
exercises, until they are perfectly familiar to the student. 
This is especially true of the irregular verb, which in nearly 
all European languages is the verb most commonly used. 
Our w^orks on grammar are singularly deficient in the sug- 
gestion of means of freeing the conversation of students from 
errors in the use of these verbs. It is only one person in a 
thousand that discriminates between " don't " and ' ' doesn't, " 
and we are constantly hearing "I had went," "We have 
saw," "The bell has rang," and so on. 

10. Syntax. — The word syntax is derived from syntaxis, 
a Greek military term meaning to draw up into line a body 
of soldiers. In a similar manner words are arranged, each 
word in its proper place, to form a sentence expressing in 
the best possible manner a complete thought. The sentence, 
being the unit of thought and language, should be fully 
treated, not only in the ideal textbook on grammar and 



§ 3 PEDAGOGICS OF GRAMMAR. 11 

language, but also in every other work on the same subject. 
By varieties of construction, and by component elements, 
one author's work may be distinguished from that of 
another. The field for the student is here a large one. It 
unites the two uses of a study as they are indicated by Mr. 
Spencer — discipline and practical utility. With respect to 
the value of the study of the sentence as furnishing the 
most excellent mental discipline, there is, among educators, 
no longer any material difference of opinion. Not even 
psychology or the higher mathematics can yield better 
results. Moreover, in dealing with the question of best 
arrangement of the elements of a sentence, to the end of 
securing the greatest smoothness, and the maximum of 
force and clearness, literary taste is developed. This is a 
side of the mind that is not addressed by the studies men- 
tioned above. The possible varieties of sentence structure 
are infinite ; hence, the fascination the study of it yields to a 
mind that delights in generalization and classification — as all 
normal minds do. 

If any phase of the study of grammar does really teach the 
pupil "to speak and write the English language coiTectly, " 
and, it may be added, to read and u)idcr stand it with keener 
perception, it is the study of the sentence. Professor Bain 
speaks of the extraordinary profit that accrues to the student 
from exercises in rearranging the parts of an involved sen- 
tence, the aim being to secure the best possible disposition 
of its constituent words, phrases, and clauses. If, besides, the 
student be required to give reasons for his various arrange- 
ments, the practice will surely, sooner or later, affect for the 
better his own sentences, render his choice of words more 
discriminating, and the action of his mind more logical and 
deliberate. 

A training of this kind has a market value, and may be 
placed ainong the practical utilities — the things that go to 
enhance the student's chances of success in life. For there 
is perhaps no way in which a man may be so accurately 
gauged as by his choice and arrangement of words, and by 
the matter and logical sequence of his thought. So that, in 



12 PEDAGOGICvS OF GRAMMAR. § 3 

its best development, the study of grammar and language 
realizes the double purpose of mental discipline and practi- 
cal utility, and it is, therefore, a subject that ranks very high 
in educational value. 

1 1 . Sentences Comblnecl in Composition.^ — Clearness, 
ease, force, smoothness, and logical sequence are most easily 
acquired by practice in the construction and arrangement of 
sentences in the various forms of composition. 

Of course there are many conditions — some of mind or 
idiosyncrasy, others of training — requisite to excellence in 
speaking and writing our mother tongue. But, given that 
one has thoughts, their effective expression is much enhanced 
by a previous training in the rationale of the sentence. It 
is generally conceded that any one whose vocal organs are 
normal may, by persistent practice, gain at least a fair pro- 
ficiency in vocal music. So also may one learn to express 
himself well, either in speech or writing, even if nature has 
withheld from him what the phrenologists call the faculty of 
language — provided, only, that he is capable of consecutive 
thought. Unfortunately — or fortunately — he that lacks nat- 
lu-al aptitudes in any direction is always reluctant to labor 
for excellence in that direction. 

12. Rlietoric. — It is particularly when we come to com- 
bine sentences into extended composition that rhetoric in its 
completeness enters into consideration. With the sentence, 
incidental questions relating to rhetoric occur, but in the 
paragraph, the poem, and other combinations of sentences, 
the sway of rhetoric becomes paramount. Even if grammar 
should stop short with the sentence, it is difficult to see how 
rhetoric can be banished from grammar. 

Again, the teacher can scarcely find justification for send- 
ing pupils out into the world with no knowledge of letter 
writing and business forms, and there seems to be no good 
reason why composition teaching should not be extended so 
as to comprehend some of their more elaborate and difficult 
varieties. 



§ 3 PEDAGOGICS OF GRAMMAR. 13 

With pupils in advanced grammar there should be no 
special difficulty in recognizing the various qualities of style, 
and the more common and useful figures of speech. They 
can easily appreciate the difference between the jerky style 
of Carlyle and the majestic sonorousness of Johnson, Addi- 
son, and Irving; between the prose-poetry of Dickens, say, 
in his Christmas Stories, his Death of Paul Dombey, and of 
Little Nell, and the matter-of-fact, straightforward, but 
elegant narrative of Scott. Access to the works of English 
classical writers is so easy that there need be no lack of mate- 
rial upon which to exercise the judgment of students. 

13. Prosody. — For exercises in grammar, selections 
from the poets are so commonly made by teachers that 
metrical considerations with reference to them can scarcely 
be passed over without attention. There are, however, so 
many varieties of feet and meter, and most of them occur in 
English verse so infrequently, that only those most used 
need be given. In the matter of the poetical feet found in 
many of our works on grammar, there is a striking illustra- 
tion of the influence of the Latin and the Greek grammars in 
shaping the grammar of our "grammarless tongue." For 
there is scarcely a poetical foot found in Horace or Pindar 
that is not found in the prosody of our English grammars, 
although many of them it is impossible to exemplify by 
quotations from our own poets. Only a few of them are in 
common use, and with these the student should be made 
familiar. Of these, particular attention should be given to 
the trochee, tambiis, spondee, dactyl, and aiiapest. With 
these few feet, it is wonderful what a striking and excel- 
lent variety of English verse has been constructed. No one 
M^ould, without examination, suspect that, with the excep- 
tion of a single long syllable at the end of an occasional line, 
poems so apparently unlike metrically as Poe's "Raven" 
and his " Bells " are both entirely trochaic. 

Pupils should be required to indicate the feet in poetical 
selections and should be exercised in scansion. They should 
mark, also, the place of cesural pauses, especially in blank 



14 PEDAGOGICS OF GRAMMAR. § 3 

verse; and it is worth the time and pains to have them 
understand what is meant by sonnet, satire, epigram, epic, 
ode, drama, comedy, tragedy, etc. Illustrations of these are 
easily found, and by knowing their form and name, added 
interest is given to their study. 

The conversion of metaphors into similes and the reverse, 
and other exercises with the figures of rhetoric, are all in 
line with the ordinary work in advanced grammar ; they are, 
besides, a means of cultivating a taste for elegant literature. 

This extension of the work of prosody, it may be said, 
belongs to the subject of rhetoric; but so few pupils in our 
common schools ever study that division of language work, 
that so much of it as is indicated above should be included in 
our textbooks on grammar. Besides, this will be much less 
in extent than the matter that is usually given under the 
subject of prosody. 

14. Capitals and PiinetTiation. — It is self-evident that 
no work on grammar should fail to note the rules for the use 
of capitals and punctuation. Capitals are not mere embel- 
lishments of printed and written language. While they add 
to the appearance of the printed page, — that being their 
principal function, — they often exert subtle effects upon the 
sense of a passage. The rules for their use are few and defi- 
nite. How to use them, therefore, is a matter easy of 
acquisition, though carelessness has intruded them into many 
places where they do not belong. For example, our text- 
books, our general literature, our newspapers, print the word 
state, and many others, with initial capitals. The following 
is taken " from a copy of the Constitution of the United 
States as printed in one of our school textbooks on history: 

" Section IV. — The United States shall guarantee to every State in 
this Union a republican form of government, and shall protect each of 
them against invasion, and on application of the Legislature, or of the 
executive (when the Legislature cannot be convened) against domestic 
violence." 

There is no good reason why state and legislature, as 
used in this place, should begin with capitals. The 



§3 PEDAGOGICS OF GRAMMAR. 15 

student will notice, in the foregoing, that while legislature 
begins with a capital, it is otherwise with executive. A 
good rule might be added to those ordinarily given : 

When there is doubt wJiether or not a capital letter should 
be used, a small letter should be preferred. 

The German language formerly distinguished all nouns by 
beginning them with capital letters, but in German books 
lately printed, this practice has, in general, been abandoned. 
There is no doubt that modern usage is drifting away from 
the use of unnecessary capitals. 

In the matter of punctuation it must not be imagined by 
the student that there is a code of hard-and-fast rules about 
which all the English-speaking world is agreed. Such, 
imfortunately, is not the case. Innumerable treatises on 
punctuation have been wn^itten, but while they agree in the 
main, in many respects they show striking differences. 
Thus, some authorities would punctuate a series with a 
comma before the and that precedes the last item in the 
series; others omit the comma. " Milk, cream, cheese, and 
butter are sold in this dairy." 

In this utilitarian age it has been discovered that punctua- 
tion is solely and simply for the purpose of making the sense 
more certain. In consonance with this purpose, in the books 
issued by those publishers whose usage is regarded as 
authority, we find punctuation omitted from title pages, 
heads of chapters, running titles at the tops of pages, and, in 
short, from everything the meaning of which is sufficiently 
definite without it. This practice has been growing for only 
a very few years, but it is doubtless one that has come to 
stay. 

If the student will note carefully the punctuation by 
dift'erent authors, he will find that each writer has his own 
notions about it. Even the same author differs in the 
punctuation of his own books written a few years apart. It 
looks as if, after writing one book, he had been studying 
the subject in a manual composed by some one having 
views at variance with his own. For example, Dickens, 
in some of his books, uses the colon incessantly; in others, 



16 PEDAGOGICS OF GRAMMAR. § 3 

it is rarely found. Sir Walter Scott is perhaps the most 
careful and consistent, in this matter, among classical 
writers. 

It may be remarked, moreover, that nearly all writers 
overpunctuate, and that most of them place punctuation 
marks not by rule, but by ear. That is to say, they are 
placed where pauses should occur if the matter were read 
aloiid. Some one has formulated the following excellent 
rule for the comma — the most abused of all marks of 
punctuation : 

If in doubt ivlictJicr to use a couima or not, omit it. 

15. Slight Need for the Mark of lilxelaniation. — 

Among the various marks of punctuation there is none that 
would be less missed, if its use were discontinued, than the 
exclamation point — the wonder mark, as some one calls it. 
Just as bodily repose is regarded in good society as an indi- 
cation of culture and refinement, so mental repose — the 
absence of emotion and wonder— {■& deemed a sign of mental 
refinement. The child, in his first attempts at spoken lan- 
guage, uses interjectional expressions almost exclusively. 
Gradually, as his intelligence increases, he expresses his 
thought in categorical sentences, empty of emotion. What 
should we think of the charge of a judge if it were punctu- 
ated with interjections ? The judicial and the philosophical 
mind does not need the interjection. Most of the sentences 
with which it is used are better if punctuated with the period 
or the interrogation point. 

The gentleman expresses his thought as a gentleman, in 
passionless, well balanced sentences; the prize fighter and 
the street Arab require the interjection; and the school girl 
cannot get along without her Oh my's! and her Dear me's! 

As civilization advances, the interjection is less and less 
used. Many of our best authors rarely employ it. AH of 
our hopes and fears, our passions and compassions, our loves 
and hates should be formulated and dominated by the intel- 
lect; if this were done, the emotion involved would not need 
to be marked by the exclamation. 



PEDAGOGICS OF GRAMMAR. 17 

THE se:n^tekce. 



GENERAIi C0]V8IDERATI0:NS. 

16. The Unit of Tlioxiglit. — It has already been said 
that the sentence is the nnit of thought, just as the word is 
the unit of the sentence. Every composition can be resolved 
into distinct sentences, each of which expresses a complete 
thought. The thought expressed in a sentence may be true 
or false, but if the sentence is constructed in accordance with 
the laws of language, it is none the less a sentence. Some of 
our authors insist that the sentence must make "complete 
sense. " A sentence may make complete nonsense^ and yet be 
a proper sentence. 

The circle is square is just as much a sentence as if it 
expressed a truth. Indeed, if the works of at least some of 
our authors were judged from the standpoint of "complete 
sense," there would be very few sentences found in them. 
Truth and falsehood have nothing whatever to do with the 
question whether a group of related words does or does not 
form a sentence. 

17. Saxon Words. — We frequently hear that the prefer- 
ence is to be given to Saxon words rather than to those 
derived from the Latin and the Greek languages, and to those of 
Norman-French origin. The Bible, Shakespeare, and Bunyan 
are cited as examples in which the vSaxon element predomi- 
nates. But since those works came into existence, the world 
has been advancing. Its requirements now in the matter of 
language are different from what they were at that time. 
The vSaxon is homely and roundabout; and while it is the 
best for pathos, it lacks the precision and definiteness of the 
language generally employed by writers of today. Shake- 
speare, when he rises highest, draws most freely from Latin 
and Norman-French. The truth is that language is constantly 
imdergoing a process of evolution, and that our vocabulary 
of a century or two ago would not meet the requirements of 



18 PEDAGOGICS OF GRAMMAR. § 3 

today. And then, too, we are apt to exaggerate the excel- 
lence of that which bears upon it the impress of age. As we 
grow old, we take our places in the ranks of those whom 
Horace refers to as Laiidatorcs tciiiporis acti — the eulogists 
of time gone by. Our language today is better than it was 
when Shakespeare wrote, and if he were with us now, to do 
again the work that made his name immortal, he would 
undoubtedly do it better. As the race evolves, everything 
keeps pace with its progress — science, invention, education, 
language. 

We must not forget what .some one calls "the perspective 
of history. " Crime seems to have increased in the world. 
It is only because there are more people in the world, and 
because our means of information are better. 

A good rule for composing English sentences might be 
given as follows: 

Put jour tliougJit in such ivords asiuill exact Iv express your 
iiicaiiiug. 

Don't trouble yourself about the origin of the words, so 
long as they are of good repute. Let them be Latin, 
Greek, French, Teutonic, anything, provided only that they 
have the warrant of good usage and meet the requirement 
of your thought. Thought must not be subordinated to 
words. 

18. Classification of Sentences Witli Respect to 

Use. — With respect to use or function, sentences a:e usu- 
ally classified as declarative, interrogative, imperative, and 
exclamatory. However they may be punctuated, exclama- 
tory sentences are declarative, interrogative, or imperative. 

" How sweet the moonlight sleeps upon this bank ! " (Declarative.) 

" What are the wild waves saying!" (Interrogative.) 

" Build thee more stately mansions, O, my soul!" (Imperative.) 

The foregoing sentences, although expressive of strong 
emotion, and, therefore, exclamatory, are in fact, respect- 
ively, declarative, interrogative, and imperative. That is to 
say, when the element of strong feeling is added to the 
thought expressed in a sentence, it becomes exclamatory, 



§ 3 PEDAGOGICS OF GRAMMAR. 19 

but it is none the less to be classified as declarative, interrog- 
ative, or imperative. The division of sentences into four 
classes is absurd. The three forms mentioned above, plus 
emotion, give three others. We have, therefore, six varieties 
of sentences when they are classified with respect to use or 
function : 

1. Declarative. 1 a. Declarative-exclamatory. 

2. Interrogative. 2 a. Interrogative-exclamatory. 

3. Imperative. 3 a. Imperative-exclamatory. 

19. Exclamatory Sentences to Be Avoided. — The 

g'radations of emotion are so various and uncertain, however, 
that it is by no means easy to determine when we should 
use the exclamation point. Remembering what has already 
been said concerning the exclamation, we are warranted in 
formulating' and observing the following rule : 

Ulicii tJicrc is doubt wJicthcr the cxclainaiioii point should 
or should not be used, do not use it. 

It was formerly the custom among writers to make much 
use of this point, but in later years there is a pronounced 
drift away from its employment. 

Another consideration of much weight in deciding this 
question is the fact that a sentence as rendered by different 
persons and under different circumstances may be devoid of 
emotion or it may be surcharged with it. If we are setting 
type so as to render faithfully the utterance of a professional 
elocutionist, we must punctuate in one way, but if a passage 
is thought of as read when hearers and reader are in perfect 
repose, the punctuation must be different. In other words, 
cold type and human utterance are greatly different, and if 
it were possible, they should be differently punctuated. And 
since repose — absence of passion — is in the direction of cul- 
ture, refinement, education, let us avoid as much as may be, 
the signs of emotional disturbance and excitement. Shake- 
speare, in his instruction to the players, anticipated the 
quietness and absence of demonstration that come in the 
slow evolution of the race. 

" Speak the speech, I pray you, as I pronounced it to you. 



20 PEDAGOGICS OF GRAMMAR. § 3 

trippingly on the tongue : but if you mouth it, as many of 
your players do, I had as lief the town crier spoke my lines. 
Nor do not saw the air too much with your hand, thus; but 
use all gently: for in the very torrent, tempest, and, as I 
may say, the whirlwind of passion, you must acquire and 
beget a temperance that may give it smoothness. O, it 
offends me to the soul to hear a robustious, periwig-pated 
fellow tear a passion to tatters, to very rags, to split the ears 
of the groundlings; who, for the most part, are capable of 
nothing but inexplicable dumb shows and noise. I would 
have such a fellow whipped for o'erdoing Termagant ; it out- 
herods Herod: pray you avoid it." 

The form of sentence that in Greek is called the optative, — 
the wishing sentence, — is in English only the declarative. 
' ' Would that I were a boy again ! " means only, ' ' I wish that 
I were a boy again." Sentences expressing a wish are 
usually followed by the exclamation point, though a period 
would be better. In concluding this paragraph, the writer 
would insist on the correctness of the classification of sen- 
tences as declarative, i)iterrogative, and imperative. 

30. Classiflcatioii of Sentences AVitli Respect to 
Form. — There is perhaps no subject in which grammarians 
differ so much as in what is a simple, a complex, and a com- 
pound sentence. If a sentence be judged by exactly what 
it contains, the matter, although still difficult, is much sim- 
plified. But our grammarians insist upon supplying what 
they call ellipses. Thus, "John, Henry, and William go to 
school," means, they say, "John goes to school, Henry goes 
to school, and William goes to school. " The writer thinks 
that no such thing is true. The former is a good English 
sentence, but the latter is not. Why not take our authors as 
we find them? If their sentences are faulty, they are not 
worthy of notice as specimens of English; if they are fault- 
less, do not mutilate them by supplying ellipses. "Jane 
swept the floor and washed the dishes " is the proper form in 
which this sentence should be written. But many authors 
insist that, for grammatical treatment, it should read, "Jane 



§ 3 PEDAGOGICvS OF GRAMMAR. 21 

swept the floor and {Jaiic or sJic) washed the dishes." In 
this form, they say that it is a compoiDid sentence. Others 
prefer to call it a simple sentence with a contracted or 
compound predicate. To illustrate, we quote from Pro- 
fessor Meiklejohn, one of our most scholarly writers on 
grammar: 

' ' There are three kinds of sentences : Simijle, Coiu- 
l><)iiiid, and Coiniilex. 

' ' A simple sentence is a sentence which consists of one 
subject and one predicate. 

"A simple sentence contains, and can contain, only one 
finite verb. 

"If we say, 'James and John ran off,' the sentence = 
' James ran off ' + ' John ran off. ' Hence it is called a 
contracted coniijonnd sentence — contracted in tiie 
predicate. 

" If we say, 'John jumped up and ran off,' the sentence = 
' John jumped up ' + ' John ran off.' " 

The objection to all this is that it is the for 7 n and not the 
meaning of which the grammarian must take cognizance. 
These awkward and mutilated forms are not what we ask 
our pupils to classify, but we submit to them the correct and 
approved forms chosen by the authors. 

Much difficulty is added by the fact that we must include 
in our classifications the imperative and the interrogative 
sentence. The imperative sentence rarely contains an ex- 
pressed subject. Thus, "Study your lesson," "Sit erect, 
and keep your eyes on the blackboard." These are impera- 
tive sentences, but in both the subjects are missing. Again, 
when the subject of an imperativ^e sentence .seems to be 
expressed, it is generally not the subject, but the nomina- 
tive case by address. Thus, "John, go to school," "Go, 
thou, and do likewise," "Go, you, and light those hay 
ricks." 

If, therefore, sentences are classified in accordance with 
what they really contain, and not with regard to what may 
possibly be supplied, the difficulty is much diminished. A 
declarative or an interrogative sentence regularly contains 



22 PEDAGOGICS OF GRAMMAR. § 3 

a subject and a predicate verb. A normal imperative 
sentence omits the subject, and if the omitted subject be 
supplied, the sentence becomes at once awkward and 
un-English. 

The writer ventures to offer the following classification, 
which is dominated by the principle that sentences must be 
classified in accordance zvith their expressed contents : 

1. A simple sentence is a sentence in which an action or a 
state of being is predicated of a subject. 

If the subject be represented by a short horizontal line, 
and the predicate by a roimded oblong, the varieties among 
sentences may be clearly indicated. An imperative sentence 
may be denoted by a cross through the subject line, thus 
denoting that the subject word is regularly omitted. The 
fact that a sentence is strongly exclamatory may be shown 
by an exclamation mark; that it is declarative, by a period; 
and that it is interrogative, by a question mark. 

" The earth moves." " The boy is sick." ( ) • 

"Go home." " Be quiet." — X — C ) . 

" Build thee more stately mansions, O, my soul!" — x — ( ) ) 



" Who goes there ?" " When is it to be ?" 



2. A simple soitence tvitli a compound subject is a sentence 
in which an action or a state of being is predicated of two or 
more subjects, or of any one of two or more subjects. 



" Butter, eggs, and vegetables are sold in this 
market." 

"Horses, sheep, and poultry are unknown in 
the island." 

" Was Arthur, his sister, or their friend at the 
picnic ? " 



El 



;} 



§ 3 PEDAGOGICS OF GRAMMAR. 23 

3. A simple sentence with a eoinpoiind predicate is a sen- 
tence in which two or more actions or states of being are 
predicated of the same subject, or in which any one of two 
or more actions or states is so predicated. 

" The boy rose and offered his excuses." — 



" Wh)^ do men so envy, distrust, and fear one 
another ? " 

" He works, sleeps, or plays." 

"Be still, sad heart, and cease repining." — > 



It will be noticed that the last sentence is griven as a sim- 
ple sentence. It has already been stated that the imperative 
sentence regularly omits its subject. When several predica- 
tions are thus made of the same subject in an imperative sen- 
tence, it shotild be regarded as simple. 

4. A simple sentence with subject and predicate compouud 
is a .sentence having two or more subjects connected by con- 
junctions expressed or understood, and two or more predi- 
cates connected in the same way. 

'The boy, his sister, and tlieir cousin go to 1 C ) \ 

school and recite their lessons." J C ) J ' 

5. A compound sentence is a sentence composed of two or 
more simple sentences of equal rank, and capable of making 
complete sense when they stand alone. vSttch simple sen- 
tences are connected by a coordinate conjunction, expressed 
or understood, and when so united these simple .sentences are 
called clauses. 

"The teacher gave out a difficult example, but the well trained 
class solved it very readily." 
" One sows, another reaps." 
" The sun went down, and the moon soon rose round and beautiful." 

The teacher will see that the varieties of compound sen- 
tences are practically inexhaustible. It must be ob.served that 
a compound sentence may contain one or more subordinate 



24 PEDAGOGICS OF GRAMMAR. § 3 

clauses. But to be compound, a sentence must contain at 
least two principal clauses; that is, clauses that make com- 
plete sense when standing alone. 

6. A complex sentence is a sentence in which there is one 
principal clause accompanied by one or more subordinate 
modifying- clauses. 

" I will pay you when my ship comes in." 

" Who are you that build your gay palaces on my margin ? " 

In these sentences, the principal clauses are ' ' I will pay 
yovi, " and " Who are you." The subordinate, dependent, or 
modifying clauses are " when my ship comes in," and " that 
build your gay palaces on my margin. " These inferior 
clauses serve only as modifiers of the verbs in their respect- 
ive principal clauses. 

The following are other examples of complex sentences: 

"The raindrops stereotyped themselves on my beaches before a 
living creature left his footprints here." 

" Build thee more stately mansions, 
O, my soul, 
As the swift seasons roll." 

" Meanwhile, I was thinking of my hrst love 

As I had not been thinking of aught for years ; 
Till over my eyes there began to move 
Something that felt like tears." 

31. Mapi^ing' Coinpoiiiirt and Complex Sentences. 

In the mapping of compound and complex sentences nothing 
more should be attempted than to show their structure by 
clauses and to denote the connectives expressed or implied 
between the clauses. Such mapping may be made of great 
value and interest in the classroom. 

The writer believes that the following scheme will meet 
the approval of most teachers : 

1. Principal clauses should have a sign of equality at the 
beginning and the end of a heavy line indicating the clause; 

thus = i =: T/ie sun set and the nioo7i rose. 



§ 3 PEDAGOGICS OF GRAMMAR. 25 

2. Subordinate clauses should be denoted by lighter lines, 
and should be separated from independent clauses and from 
one another by the sig;i of inequality, the opening of which 
is towards the clause of which the dependent clause is a 
modifier. If a subordinate clause modifies a mere word or 
phrase, the sign of inequality should be turned towards the 
line representing the clause that contains such word or 
phrase. 

= = -f-> Tlie iiioou rose bcj07-c the sun set. 



i-^ 



< = = If the day is fine, ^ve shall go. 

f+> 



+ Before I leave I shall see yoii, if 

> — — 



you are at leisure and wish me to come. 

== — ■ — =; y^ 1 kiio%v a bank 70 hereon the ivild thyme 

gr07ijs. 

3. If a principal clause is broken by one or more con- 
tained subordinate clauses, the fact should be shown as 
follows : 

— 1-> < = The house that Jack bid it stood by 



the sea. 



+> <i 

+ \ = T\\Q n\QiXi\oyv that ?ny father 07i'ned 



and in 7i>hieh the school house stood had a trout stream flo^ving 
through it. 

<-l — < ^ h> — — < = When 7ve said that ice 

had lost our 7vay, the farmer's Avife, Avith a smile that made 
us feel at home, invited us to stay to dinner. 

4. If a clause is used in apposition, or for any other 
reason is out of grammatical relation to the other clauses of 
a sentence, the fact is indicated by a wavy line. Clauses so 
used commonly have the value of subordinate clauses, for 



26 PEDAGOGICS OF GRAMMAR. § 3 

their use is to explain the meaning of some word or phrase 
or clause. They are said to be used independently. 

= = >^'--'^~ "They asked the old doctor the very trouble- 
some question, ' Where did Cain get his wife ?' ' 

"In the serene expression of her face he read the divine beatitude, 
'Blessed are t lie pure in heart.' " 



= +> 1-= = " Whence did we come? 



whither are we going?: these are questions that are continually 
asked, but no person has ever been found able to answer them 
satisfactorily." 

33. Subject and Predicate. — No grammarian has thus 
far been able to give a satisfactory definition of the subject 
or the predicate of a sentence. The difficulty is chiefly 
owing to the fact that we have three forms of sentences — the 
declarative, the interrogative., and the imperative. The first 
states, or declares; the second expresses an inquiry; the 
third consists of a command or an entreaty. No device of 
language can be foimd that will include all these. One 
author says: " The subject of a sentence 7S wliat we speak 
about.'' "John saws wood." But we speak about ivood\\QXQ 
just as much as we do about John. And then, too, accord- 
ing to the definition, it is the person John, and not the ivord 
John, that is the subject. 

The teacher cannot emphasize too much the fact that the 
subject of a sentence consists of one or more ivords denoting 
a thing. Hold up a book in your class and ask your pupils 
to say what part of speech it is, and they will invariably call 
it a noun. But they are not to be blamed when it is the " Pro- 
fessor of the Theory, History, and Practice of Education " 
in one of the greatest universities of Scotland that gives us 
the definition quoted above — " TJie subject of a sentence is 
what %ve speak about. " 

The same author says: " The predicate in a sentence is 



§3 



PEDAGOGICvS OF GRAMMAR. 



27 



zvhat zve say about the subject.''' Now, a little reflection will 
make it clear that in a declarative sentence we say, but in the 
interrogative and the imperative sentence, we do nothing of 
the kind. Moreover, it takes all the zvords in a sentence to say 
anything of a subject. The predicate has no more important 
part in saying things than the subject. 

In short, subject and predicate, in grammar, never have 
been, and perhaps never can be, defined. The best way out 
of the difficulty is to have our pupils know which words in a 
sentence make up the subject, and which the predicate. 

One of our late writers on g. ammar and language, recog- 
nizing, apparently, the utter futility of attempting to define 
subject QXid predicate, resorts to a plan like the following in 
order to have pupils understand what these words mean: 



subjects: 

Birds 

Good boys 

The "Mill on the Floss" 

" A bird in the hand 

The house that Jack built 



predicates: 
fly. 

obey their parents. 
was written by George Eliot, 
is worth two in the bush." 
was a house of the imagination. 



a:n^ai.ysis of sextexces. 

33. Distinction Between Mapi)inj>; and Analysis. — 

The foregoing scheme considers only the large parts that 
make up a sentence. For the simple sentence, these parts 
are the subject and predicate ; for the complex and the com- 
pound sentences, it is their clause structure that is indicated 
by mapping. This general analysis is perhaps of more value 
to the student than the more elaborate and detailed methods 
that are given in nearly all grammars published in recent 
years. 

In mappings sentences nothing more need be attempted 
than is indicated above. The three kinds of simple sen- 
tences — declarative, interrogative, and imperative — can be 
sufficiently distinguislied by using, at the end of their out- 
line, a period, a question mark, or an exclamation point. If 



28 PEDAGOGICS OF GRAMMAR. § 3 

strong emotion is to be superadded, an exclamation point, in 
addition to the ordinary mark, may indicate it. 

Declarative sentence. CZD. 

Declarative sentence, plus emotion. - — ( ) i 

Interrogative sentence. ■ ■ ( ) ? 

Interrogative sentence, plus emotion. ( ) ?l 

Imperative sentence. x ( ) 

Imperative sentence, plus emotion. — )f- ( )[ 

A cross denotes that the subject is not expressed. 
The analysis of a sentence requires not only that the use, 
or function, and the relation of its larger elements — its 
phrases and clauses — should be clearly indicated, but also 
that the oiSce of every word should be denoted. This may 
be done entirely in written or spoken language ; but during 
the last few years many systems of diagrams have been 
devised for this piirpose. 

34. Analysis by Diagrams. — Professor Bain, in his 
" Education as a Science," argues, not with much force, the 
writer thinks, against the employment of the terms analysis 
and synthesis. "To express," he says, "the conduct of any 
school lesson under either of the terms anal3^sis and [or?] 
synthesis, is to produce the utmost confusion in the mind of 
a young teacher, as everything that the words cover is con- 
veyed by other names, more expressive and more intelligible. 
Such are description, explanation, abstraction, induction, 
deduction." The writer thinks that the contrary is true. 
Very rarely are the words that Mr. Bain would substitute 
for those in question well imderstood by young teachers. 

" Take down a watch, analysis ; put it up, synthesis," says 
Lord Brougham. 

Among the teachers of the United States, it is in precisely 
this sense that these words are understood and employed. 
To take a sentence apart, an example in arithmetic or an 
argument, is analysis. 

Nearly every author of a work on graiumar or language 
lessons has a scheme of picturing minutely the relations that 
exist among the words, phrases, and clauses that are united 



§ 3 PEDAGOGICS OF GRAMMAR. 29 

to form sentences. Almost all of these schemes are open to 
objection, and the difficulties that beset the subject are n(;t 
easy to remedy. Sentences should not be dismembered 
in analysis, but should be preserved just as their authors 
left them. Moreover, the scheme of analysis should le .'■•o 
simple as to be easily intelligible. The author ventures to 
offer the following method of sentential analysis — examples 
first and explanation afterwards. It may be accompanied, 
or not, by the general mapping of sentences, as already 
explained. 

Examples sufficiently numerous are given to indicate fully 
the method of analyzing sentences without dismembering 
them. Several eminent writers on education insist that this 
should be realized in every system of diagrams. Doubtless 
some better method of doing this may be found later; but, 
for the present, the writer knows of nothing better. 

!25. Models of Analysis. — 



ir 



1. The (earth) [is] round. 



2. [Was] (Barrabas) a robber? 



CZ3- 



JI 1 

3. (Paul), the apostle, [preached] upon Mars Hill. 

t 220 t I — 



+ 



-< 



IV 



4. (That the (earth) [is] round) [is] no longer [disputed]. 



30 PEDAGOGICS OF GRAMMAR. 



= +>- 



+ _£ 1 I IL_ 

5. (He) [died] 'when the (tide) [went] out. 



CD. 



6. (To be), [contents] his natural desire. 

The object of a transitive verb— in this sentence, desire— 
may be connected to the verb to show that it has on the 
verb a modifying efeect. Example 10 shows how the con- 
nection is made. 



7. 


+ _L 4 

If the (sky) [fall], ; (we) [shall catch] sparrows. 

1 T 


— 


l( ) 


8. 


Seventeen hundred, (it) [came] and [found] 




111 + 




The deacon's masterpiece strong and sound. 








.....< ^.,.. 


9. 


1 i _L 1 ^ 
(I) [met] a traveler from an antique land 

t f 1 




+ 1 1 1 1 i 




'>(Who) [said] : Two vast and trunkless (legs) of stone 

t 1 

[Stand] in the desert. 

t 1 



PEDAGOGICS OF GRAMMAR. 31 

4- 



10, A little (learning) [is] a dangerous thing; 

T -^ t T I I 

+ I 1] L I ^ 

[Drink] deep, or [touch] not the Pierian spring. 

t =r- t ^r= 



11. =Milton, (thou) [shouldst be living] at this hour; 

I t 



J 1 r^ 

=(England) [hath] need of thee: ^=( she) [is] a fen 

J 

1 + 

Of stagnant waters :=( altar, sword, and pen, 

1 t 



I I I 4- 

Fireside, the heroic wealth of hall and bower, ) 



[Have forfeited] their ancient English dower 
_J 



Of inward happiness, zz 

I t 



This sentence consists of four clauses of equal rank sepa- 
rated in the diagram by signs of equality. 



12. - }+> ^ +> 



JT V 



The (world) [will] little [note] nor long [remember] what (we) [say] here; 

+ + i — Zl_ 

but (it) [can] never [forget] what (they) [did] here. 



32 



PEDAGOGICS OF GRAMMAR. 



The first wJiat is the object of say—ive say what; the 
second is the object of did — tJicy did iv/iat. In like manner, 
luhat ii'e say here is the object of reiiiembcr, and i<j]iat tJicy 
did here is the object of can forget. 

13. ^. 



+ ^ I _iz — \ 

But (grief) [should be] the instructor of the wise; 

"TZ 1 1 



4- 



(Sorrow) [is] knowledge : (they) (who) [know] the most 

t ^ =^ 



[Must mourn] the deepest o'er the fatal truth, 

t I • I 



The (Tree) of Knowledge [is J not that of Life. 

~IZ 1 I — ^ — I — 



26. Revie^v of Details in Analyzing. — 

1. The Subject. 

The subject of a principal clause is enclosed in Jieavy marks 
of parenthesis, ( ). 

The subject of a subordinate clause is enclosed in light 
marks of parenthesis, ( ). 

A subject that is clearly implied but not expressed maybe 
denoted by a caret within marks of parenthesis, (^), (^). 

2. The Predicate. 

The predicate of a principal clause is enclosed in heavy 
brackets, [ ]. 

The predicate of a subordinate clause is enclosed in smaller 
light brackets, [ ]■ 

When a predicate consisting of two or more words is 
broken by an interposed word or phrase, the fact is shown as 
below : 

" The unwearied (sun) from day to day 
[Does] his Creator's power [display]." 



§ 3 PEDAGOGICS OF GRAMMAR. 33 

3. Predicate Complement. 

The object of a transitive verb is denoted by two parallel 
lines bcloiu it. 

" We saw the moon." 



A predicate noun should have two parallel lines above it. 



" The boy is a gentleman." 

A predicate adjective is shown by a straight line above a 
wavy line, -. 



These men are wise and honorable. 



The squire looked rosy and healthy and seemed happy. 

4. Modifiers. 

A modified element is connected with its modifier by an 
arrow line, [ \ 

-+L I ^ 1 

The (place) where shining (vsoiils) [have passed] 

~n 1 I 

[imbibes] a grace beyond mere earth. 

t =f ^ I 

This sentence shows three kinds of modifiers: zcords, a 
plirasc, and a clause. 

(1) Words. The is an adjective modifier oi place; shining, 
of souls; a, of grace ; and mere, of earth. JVhere is a con- 
junctive adverb modifying ha^'c passed. 

(2) Phrase, beyond mere earth is an adjective phrase, 
modifying grace. 

(3) Clause, zi'here shining souls have passed is an adjec- 
tive clause, modifying /Arr*:'. 

5. Connective Elements. 

Conjunctions, conjunctive adverbs, and relative pronouns 
used to connect words, phrases, or clauses are marked by a 
plus sign, +. If they have any other office, it is indicated 
accordingly. 



34 PEDAGOGICS OF GRAMMAR. § 3 

+ 
" The (ship) (that) [was blown] up at Havana [was] the ' Maine.' " 

+ + + 

Tell us where you went and whom you saw. 

— [^ f = T=^ t 

In the first sentence, t/iat is both a connective and the sub- 
ject of a verb in a subordinate clause. The former function 
is denoted by the sign +; the latter, by enclosing it in light 
marks of parenthesis. 

In the second sentence, a/id is a mere conjimction, having 
no other value than that of a connective. Where is a con- 
jimctive adverb introducing the clause in which it occurs, 
and connecting it to the rest of the sentence; besides this 
office, it is an adverbial modifier of %vent. Whom is a rela- 
tive pronoun used as a connective and as the object of saw. 

G. Independent Elements. 

When any word, phrase, or clause is used without gram- 
matical relation to other elements of the sentence in which 
it is found ; that is, when it is independent, the fact is shown 

by a wavy line either above it or below it, . 

As has been remarked in a preceding article, independent 
elements generally have, in some nieasm-e, the value of 
modifiers; they are, therefore, not entirely without gram- 
matical relation to the rest of the sentence where they 
occur. The interjection is an example of almost complete 
independence; yet the effect of a sentence containing an 
interjection is not quite the same as it is when the interjec- 
tion is omitted. 



I 



r 



(Botany), the science of plants, [is] a very interesting study. 



1 . / X . .,..+. 



'Time! ah, the treasure! (l) [have lost] it;" and (he) [died]. 



PEDAGOGICS OF GRAMMAR. 35 



Backward, (^/\ J [turn] backward, time, in your flight. 

r— t I ' ■ I " 



Ye crags and peaks, (IjL'mJ with you once again. 



Remarks on tlie Foregoing Method. — It is believed 
that every possible grammatical relation may be clearly 
indicated by the foregoing method of analyzing sentences. 
By long trial the writer knows that it may be used with 
success in the classroom. It avoids the serious objection 
of requiring that the sentence, in order to be analyzed, must 
be separated into fragments that the pupil cannot prop- 
erly recompose. Professor Bain is especially emphatic in 
his criticism of those methods of making diagrams that 
displace the words from their stations in sentences. This 
method is as readily applicable to very long sentences 
and to paragraphs as to the shorter sentences usually 
found in our grammars. A very valuable use of it can 
be made by requiring pupils to copy and analyze long pas- 
sages from the classical writers. A good plan is for the 
teacher to accumulate a collection of classified sentences 
suitable for his grade. These, preserved in a note book, 
are a great convenience. In every case they should be 
taken unchanged from our classical writers. In the first 
teaching of analysis, the general outline, or mapping, is 
the easier and better. The minute analysis should come 
later. Only after the pupil has learned to construct a 
general outline of a sentence, indicating its clauses and 
their relations, should he be required to give its minute 
analysis. 

For the purpose of becoming familiar with this system of 
analysis the student should map and diagram the following 
selections, and he should do it without dismembering the 
sentences; 



36 PEDAGOGICS OF GRAMMAR. § 3 

37. Selections for Mapping: and Analysis. — 

I. "Many lineaments of the character of the man were early 
discerned in the child." 

3. "Neither climate nor poverty, neither study nor the sorrows of 
a homesick exile could tame the desperate audacity of his spirit." 

3. " Come read to me some poem, 

Some simple and heartfelt lay. 
That shall soothe this restless spirit 
And banish the cares of day." 
{Come read are equivalent to anne and read.) 

4. " Here rests his head upon the lap of earth, 

A youth to fortune and to fame unknown." 

5. " All that I have, and all that I am, and all that I hope in this 
life I am now ready to stake upon it." 

6. " On a sudden, open fly 
With impetuous recoil and jarring sounds 
The infernal doors." 

7. "I could never quite under.stand how any man could prefer to 
be idle." 

8. " The historical essay must be flexible, and it may be light in 
tone." 

9. " A sentence is the first complete organic product of thinking, 
and in its precision and strength it reveals the vigor of the process 
iinder which it has arisen." 

10. "A pure mind is the noblest possession." 

II. " Make haste slowly; send your work back to the anvil twenty 
times, if necessary." 

{Tf necessary = if it is necessary.) 

12. " What hoi^e has innocence when her judges are corrupted ?" 

IB. "Thou wert my guide, philosopher, and friend." 

14. " He raised a mortal to the skies; she drew an angel down." 

15. " He spoke, and into every heart his words carried new strength 
and courage." 

16. " He is ai-med without that's innocent within." 

17. " Were such things here as we do speak about; 

Or have we eaten on the insane root 
That takes the reason prisoner ?" 

18. " For who would lose, though full of pain, 

This intellectual being, those thoughts that wander 
Through eternity ?" 

19. " No wise man ever thought that a traitor should be trusted." 

20. " My tongue within my lips I rein, 

For who talks much must talk in vain." 



PEDAGOGICS OF GRAMMAR. 37 



MEANING OF TERMS. 

38. Modification in Grammar. — The analysis of sen- 
tences leads of necessity to the question of the modification 
of one part of speech by another, of phrases by phrases, and 
of clauses by clauses, and so on. Most grammarians employ 
the words modify, qualify, and limit so as to make them seem 
to have the same meaning. Thus, they say that a noun is 
modified, qualified, or limited by an adjective. Indeed, there 
is much confusion in the use of these terms, though, per- 
haps, not very great importance should be attached to this 
fact. But when it is added that pupils have a very nebulous 
notion of what the terms mean, although they use them 
glibly and constantly, it becomes a matter of much impor- 
tance that the exact sense of the terms should be explained. 

39. Tlie Woi'cl " Modify." — The term modify contains 
the Latin word modus, a measure. Hence, literally, to mod- 
ify is to measure the extent in which a meaning or anything 
else is to be taken or understood. For example, the word 
boy includes every conceivable boy, real or ideal, large or 
small, living or dead. The word small when prefixed to boy 
excludes the greater number of boys that may be designated 
by the unmodified word; that is, the word small lessens 
the measure or extension of the term boy to which it is 
joined. In small boy tvitJi blue eyes the measure of the 
term boy is still more diminished. In short, every added 
modifier lessens the number of objects inckided by the term, 
but adds to the definiteness of the mental picture. The 
effect in this respect is the same whether the modifying 
element is a word, a phrase, or a clause. This will be 
apparent if the student will carefully consider the following 

examples: 

the "I f by the well 

the old I by the well at home 
the old oaken I |-,,i«if-f>f J ^y the well at the home of my 

the old oaken, iron-bound i j childhood 

the old oaken, iron-bound, | | that hung by the well at the 

moss-covered J I home of my childhood 



38 PEDAGOGICS OF GRAMMAR. § 3 

On the contrary, qualities detached from a notion extend 
the list of objects to which it applies, but each such exten- 
sion in number makes the picture less vivid and definite by 
diminishing the number of characterizing- marks or qualities. 
In the one case, we have a picture in merest outline with no 
details; in the other, the picture has life and color and 
motion and relation of parts. 

These opposite spheres of notions constitute what in logic 
is known as I'xtciision and coinprcJioisioii — the former refer- 
ring to the number of objects to which a term applies, the 
latter to the number of attributes or qualities associated with 
it. Hence, we have the well known law of the inverse ratio 
between the extension and the comprehension of common 
terms, viz., Tlic greater the extension^ the less the coinpre- 
heusioji, and viee versa. 

30. The Word '' Qualify."— The word qualify is 
another term much used in grammar. It should be exactly 
understood and carefully explained by the teacher. Being 
derived from the Latin qualis — of what kind ? — it is not of 
so wide or general meaning as modify. All words modify 
that qualify, but not all modifying words qualify. Thus, in 
the expressions, red apples, some apples, five apples, all the 
adjectives modify, but, as used by most grammarians, only 
the first qualifies — denotes some quality that appeals directly 
to one or more of the senses. The term is synonymous with 
deseriptive as employed by most grammarians. Modify and 
modifying are generally used to indicate adjectival and 
adverbial functions of words, while the noun modification 
is restricted to those changes of form denoted by number, 
gender, case, declension, comparison, and conjugation. Of 
the words that contain the Latin qualts, qualify and qual- 
ifying are the only forms usually found with a technical 
meaning in the grammars. 

31. The Word *' Jjiniit.'"' — The \word limit is derived 
from the Latin limes, the root of which is limit. The literal 
meaning of the word is a cross-path. The Romans usually 



§ 3 PEDAGOGICS OF GRAMMAR. 39 

had in their fields two broad and two narrower paths cross- 
ing- at right angles. These were limitcs, but each had a 
special name. So they came to use the term in the sense of 
boundary or margin. As applied to concepts, it has refer- 
ence to anything that restricts their extension, using this 
word in its logical sense. The terms limit and modify are, 
therefore, almost exactly synonymous, but the latter has 
come to be the more generally used word. When we say 
seven men, we limit the men with reference to number; that 
is, we establish, a boundary or path that must not be crossed 
from without or from within. In a similar manner, in the 
expression good girls, the word good has the effect of inclu- 
ding — shutting in — all girls of that class, and excluding — 
shutting out — all others. To limit, therefore, is to establish 
boundaries. 

The writer has dwelt upon these terms, not only because 
of their extreme usefulness in grammar, but also because he 
has noticed that very few teachers employ them with dis- 
crimination; and when the teacher does not understand, tlie 
pupils will always be in the same condition, or in a worse 
one. 

32. Geiiei'al Modificatiou. — Again, it should be 
observed that ei'cry word in a sentence modifies the meaning 
of all the rest taken collectively and separately. When, for 
example, the ear hears the word runs, there is at once 
formed in the mind a picture of something — anything — 
performing the act of running. In the absence of informa- 
tion, the mind may supply a man, a horse, a dog, a loco- 
motive. This tendency of the mind to complete, in some 
way, imperfect mental pictures, is irresistible. If, now, the 
boy be prefixed to runs, the mental picture is inodified — its 
comprehension is widened and its extension is narrowed; man, 
horse, dog, locomotive — everything- but boy — is shut out. If 
rapidly be added, the act of running is limited to a certain man- 
ner of running by a boy ; and along the street again changes 
or modifies the mental picture. Similarly, the meaning of 
the expression / zvrite is modified — its extension is narrowed 



40 PEDAGOGICS OF GRAMMAR. § 3 

and its comprehension or definiteness is widened — when an 
object is added, / zvrite a letter. The transitive verb ivrite 
is just as really modified by the object letter as it would be 
by an adverbial modifier. And not only is ivritc modified 
by a letter, but the entire expression / ivrite as well. 

In grammar, however, we say that certain words modify 
certain other words, and not entire sentences. But in reality 
the subject modifies the predicate, and the object modifies 
both, and is itself modified both by the subject and the verb, 
taken separately or together. A word does not need to be 
an adjective or an adverb to be a modifier. In other words, 
the law of the inverse ratio between the extension and the 
comprehension of common terms applies to all sentential 
elements. Eveiy word added to a sentence makes the 
mental image more definite and diminishes the extent of 
its application. 

33. Value of Exactness and Tlioroiijifliness. — It 

would be difficult to overestimate the importance to the 
teacher of being exact and thorough; and, indeed, of know- 
ing thoroughly every subject he teaches, and the precise 
meaning of every term he uses. The' writer remembers 
hearing one of the world's greatest linguists say that it is 
better to know all about one page of a foreign language than 
to know vaguely a great many pages. One of the great 
objections to the reading of novels and newspapers is that a 
habit of skimming the surface of the meaning is formed ; and 
this habit dominates us when we should read with attention 
and intensity. Make sure, therefore, that your pupils know 
the exact meaning of the language they use, and especially 
the meaning of technical terms. Equally important is it 
that the teacher shall know exactly what the language 
means that he uses. Incomplete and imperfect concepts 
are characteristic of nearly all human knowledge. Another 
source of vagueness is the uncertain interpretations that 
different minds put upon the words we use to express our 
thought. No two persons get exactly the same idea from a 
given combination of words. Some one says that we learn 



§ 3 PEDAGOGICS OF GRAMMAR. 41 

the meaning of words not so much from the dictionary as by 
noting their context — the way in which they are used. The 
first time we meet a given word, we assume a meaning for it 
that seems to suit the use made of it. Our assumed mean- 
ing may be very different from its real meaning. Then a 
process of approximation and cliininatioii begins. We meet 
the word again, and our first notion must be corrected; and 
so time after time we ehminate elements of our first notion, 
and approximate moi'e and more nearly to the true meaning. 
If this view is correct, it follows that the best way to study a 
foreign language is to read a book in the language without 
the help of a dictionary. The first time it is read, we get a 
very imperfect notion of its contents. If we read it again, 
something is added to our previous knowledge; and after 
several readings, there will remain some words that caiaiot 
be understood from the context. Then the dictionary 
becomes useful and necessary. Having learned the 
meaning of those words, we read the book as if it were 
our mother tongue. This is an illustration of the process 
of approximation and elimination. 



AMBIGUITY. 

34. Ambifyuity From Restrictive and Coordinate 

Clauses. — In the classification of sentences, the teacher is 
often in doubt as to whether a given clause is restrictive or 
coordinate. A restrictive clause is one that merely modifies^ 
while a coordinate clause is one of equal rank with a princi- 
pal clause. " The temple tliat Solomon built stood upon 
Mount Zion. " The clause that Solomon built modifies tem- 
ple, and is therefore restrictive. This fact renders the sen- 
tence complex. But take the sentence, "The dog, ivhicJi is 
man's best friend anuvig the lower animals, is a relative of 
the wolf." The two clauses composing this sentence are 
coordinate, that is, of equal rank. The word which is 
equivalent to and he. The sentence is, therefore, compound. 
Clauses denoting tiine, place, manner, and inference are 
nearly always restrictive ; in general, clauses introduced by 



42 PEDAGOGICvS OF GRAMMAR. § 3 

conjunctive adverbs are commonly restrictive. Clauses 
introduced by the relative pronouns ivJio and tvJiicJi and their 
compounds with ever, so, soever, are nearly always coordi- 
nate; but the relative t/iat is properly used to introduce 
restrictive clauses. It is necessary, therefore, to consider 
more fully the latest authorized use of these relatives. 

35. Wlio, Wliieli, and That. — In the use of no words 
in our language do writers exercise less care than \\\i\\ those 
forming the title of this paragraph. Formerly, no serious 
attempt was made to employ them with discrimination. It 
was said that who and that should be used to relate to per- 
sons, or to things personified, and wJiieJito young cJiildr en, to 
the hnver animals, and to inanimate objects. Many of our 
later writers have adopted the following ride with reference 
to the use of these words : Use avIio and Avliich. as coordi- 
nating relative pronouns, and tliat as a restrictive relative 
pronoun. The sentences that follow will illustrate this 
important distinction : 

"The house, which cost me five thousand dollars, was 
destroyed by fire." {zuhich = and it) The sentence is com- 
pound, vsince it means, ' ' The house was destroyed by fire, 
a)id it cost me five thousand dollars." 

" The house that my father owned stood by the seashore." 
This sentence is complex. The clause that my father oivned 
is an adjective modifier of house. It is an exact eqiiivalent 
of my fat J 1 07'' s. 

"The relatives that zverc invited were at the wedding." 
The relatives tliat ivere invited = The invited relatives. 
vSentence is complex. 

"The children, who' were ver}" obedient, were allowed to 
go to the picnic. " {ivJio = and they) Compound sentence. 
They were all allowed to go to the picnic. 

"The children that are very obedient .shall have a half 
holiday. " A promise to such only as are obedient ; a complex 
sentence. 

"He that soweth the wind shall reap the whirlwind." 
Restrictive clause ; sentence complex. 



§ 3 PEDAGOGICS OF GRAMMAR. 43 

" He, who showed nie all the depths and shoals of honor, 
died yesterday. " {(ivJio = and he) Coordinate clause; com- 
pound sentence. 

" Those that live in glasshouses should not throw stones." 
Restrictive clause; complex sentence. 

' ' Those books, which I bought a year ago, have not yet 
been read." Coordinate clause, (ivliich — and thciii) 

"The books that are on the lower shelf were written by 
Dickens." Restrictive; complex sentence. 

"The boy, who had done no wrong, was punished." 
Here wlio = altliongh he. Compound sentence. 

"The members, who disliked their pastor, asked for his 
resignation." This means all the members. Compound. 

"The members that disliked their pastor left the church." 
Only some of the members are included. Complex. 

The writer believes that sufficient has been g-iven above to 
make clear the sharp distinction that should be observed in 
the use of the relative pronouns. This distinction, too, con- 
forms to the latest usage. Unless it is observed, a writer 
finds it scarcely possible to avoid ambiguity. Indeed, nearly 
all of the uncertainty of meaning that we find in our litera- 
ture comes from the use of pronouns. In the writings of 
Robert Louis Stevenson, it is scarcely possible to find a sen- 
tence where these relative pronouns are misused. One of 
our critics, speaking of the works of this writer, says: "No 
better English has been written by any other author since 
the pen fell from the tired hand of Thackeray. " If the stu- 
dent will examine vStevenson's writings, he will notice the 
almost entire exclusion of the coordinating relative pronouns, 
and will be struck with the sparing use of the restrictive 
relative pronoun. To illustrate, we quote from his beautiful 
prose poem, " Will o' the Mill." 

"That divine unrest, that old stinging trouble of humanity that 
malce all high achievement and all miserable failure, the same t/iat 
spread wings with Icarus, the same that sent Columbus into the 
desolate Atlantic " 

Here it would be difficult to omit the relative pronoun. 

" He felt as if his eyesight would be purged and 



44 PEDAGOGICS OF GRAMMAR. § 3 

clarified, as if his hearing would grow more delicate, and his breath 
would come and go with luxury." 

In this quotation we have as if for tJiat, used as a con- 
junction. Even when tJiat loses in some measure its pro- 
nominal value and becomes a mere subordinate conjunction, 
it is still used with something of the office of a pronoun. 
Thus, "He felt that etc." = "He felt this, namely, that 
etc." When, as here, tliat is used as a subordinate con- 
junction, there is an implied antecedent of the pronominal 
function that has not entirely vanished froin the Avord. 

" It was no wonder he was unhappy." 

The coordinating use of %uho and wJiicJi is illustrated in 
the following three quotations: 

"The shepherd, who makes so pretty a picture carrymg home the 

lamb, is only carrying it home for dinner." 

" I feel tongue-tied myself, who am not used to it. ' 

"He tried to prove that this was no more than a true lovers' tiff, 

which would pass off before night." 

36. Care Required in the Use of tlie Relative 
Pronoun. — It may be inferred from what has been said 
tmder the preceding topic that pronouns of every kind 
should be used sparingly, and that, when used, there should 
be no uncertainty abotit their antecedents. When there is 
only one possible antecedent, no ambiguity can result from 
the use of pronouns; but, when there are several words in a 
sentence, any one of which may be the antecedent of a sub- 
sequent pronoun, the meaning generally becomes a matter 
of conjecture. The teacher cannot overestimate the impor- 
tance of this matter. Exercises should be prepared that 
contain pronouns used ambiguously, and the pupils should 
be required to clear up the uncertainties. 

A relative should be as close as possible to its antecedent, 
and no word should be introduced between them that is 
likely to be mistaken for the antecedent. 

" Let me introduce the son of my friend, who formerly resided in 
this city." 

The antecedent of ivJio may be either son or friend. If 



S 'J 



PEDAGOGICvS OF GRAMxMAR. 45 



son is the antecedent, the ambiguity is removed by chang- 
ing to 111)' fn'i'/h/'s so//, 7i'//o etc.; \i friend, we should say 
tJic son of i/iy f/-icnd that etc. It would be still better to 
separate the descriptiv^e part: '' Let me introduce the son of 
my friend — my friend that formerly etc." 

Very frequently the predicate is improperly interposed 
between the relative and its antecedent. 

''He is well paid tliat is satisfied." ''He should not 
blame another man that himself has erred." 

Better: "He that is satisfied is well paid." "Ife that 
has erred should not blame another." 

The following are some other examples of ambiguity from 
uncertain antecedents: 

" This way will direct you to a ge//t/e///a//'s ho//se that hath 
skill to take off these burdens." Should be "to the house 
of 3. gei/tle/iia// that etc." 

"Nor better was the//- lot that fled" = " the lot of thei/i 
that fled." 

"All is not gold that glitters." Better, "Not all that 
glitters is gold." 

"Cats catch no mice that wear gloves." Write instead, 
" Cats that wear gloves catch no mice. " 

37. Exercise. — Both by means of maps and diagrams analyze 
the following sentences, being careful to distinguish between restrict- 
ive and subordinate clauses: 

1. " All that tread the earth are but a handful to the tribes that 
slumber in its bosom." 

2. " The Romans were the best soldiers and the wisest lawgivers 
that the world has ever seen." 

3. " The first Napoleon, whom tlie English banished to St. Helena, 
died there in the year 1821." 

4. "... a lie which is all a lie may be met and fought with 

outright, 
But a lie which is part a truth is a harder matter to fight." 
( T/iat would be better than lohich here in both places.) 

5. " The saddest thing that can befall a soul is when it loses faith 
in God and woman." 

fi. " It is alwavs right that a man should be able to render a reason 
for the faith that is within him." 



46 PEDAGOGICS OF GRAMMAR. § 3 

7. " He that does one fault at first and lies to hide it makes it two." 

8. "It left a sting behind that wrought him endless pain." 

9. " There were the vast lips, which, if they could have spoken, 
would have rolled their thunder accents from one end of the valley to 
the other." 

10. " How can a country whose very name suggests to us move- 
ment and progress be governed by a system and under an instrument 
which remains the same from year to year and from century to cen- 
tury ?" 

SYNTHESIS. 

38. Synthesis of Sentential Elements. — In teaching 
the structure of sentences, synthesis is just as important 
and just as interesting as analysis. Professor Bain, indeed, 
objects to the use, in grammar, of the term synthesis, 
although it is pretty clear that his protest is based upon 
nothing stronger than the fact of its metaphysical use. 
But, in the United States, at least, a work on language that 
should omit exercises in synthesis would have but little 
chance of success against competitors. As has been said, 
the meaning of the word is the opposite of the word analy- 
sis. It is derived from two Greek words: syn, together, and 
thesis, a placing or putting — a putting together. If the 
parts of a watch or a locomotive were all at hand, but disar- 
ranged, and one were to arrange them — put them together 
— the operation would illustrate what is meant by synthesis. 
Any arranging of sentential elements — words, phrases, and 
clauses — so as properly to express thought, is synthesis. 
Hence, any composition in which the writer properly 
arranges the elements of thought is an exercise in synthe- 
sis. The same is true when the teacher finds the thought, 
or the disarranged sentential elements that, properly put 
together, will express a thought. There is a form of puzzle, 
much delighted in by children. It is known as the dissected 
pieture. A picture on a large piece of cardboard is cut into 
pieces of different shapes, and the child is required to arrange 
the parts so as to show the picture as it was at first. This 
suggests a valuable exercise in verbal synthesis. The writer 
once knew a very intelligent teacher that provided herself 



§ 3 PEDAGOGICS OF GRAMMAR. 47 

with as many small paper boxes as there were pupils in her 
class; in each box she put the words and phrases of a sen- 
tence, together with the proper punctuation marks. The 
sentential elements were neatly written upon bristol board. 
The boxes having been distributed, each pupil was required 
to arrange the contents of his box so as to form a sentence. 
The work of preparing the boxes and their contents was one 
not involving the expenditure of much time or money, and 
the enjoyment and profit to the children were of the highest. 
Of course the teacher will see in this a scheme that can be 
carried down to the lowest primary grade, and used as an 
adjunct in teaching reading and in furnishing a vocabulary. 
In these exercises the sentential elements may be given 
as words, or the phrases may be entire — a matter to be 
governed by the grade of the class. For the lowest grades 
"Mother Goose " or other similar classic for children is a good 
source from which to get the material for this exercise. Of 
course, for higher grades, more difficult selections may be 
made. After the various sentences formed during an exer- 
cise have been examined and approved by the teadier, a 
writing lesson may follow, and in it the sentences may be 
i;sed as copies. Two such sets of 50 each should last 100 days. 

39. Syiitlietic Kxercise for Increasinj>" tlie Vocabu- 
laries of I'lipils. — Again, take not more than five new words 
daily for four days a week. They should be assigned the 
day before they are to be used. Of course the children will 
talk about their meaning, and so the process of approxima- 
tion and elimination will begin. The words are written 
upon the board and numbered. The teacher directs that 
the pupils in the first row of desks shall take the first word 
and introduce it in sentences so as to show that they have 
learned the meaning of the word — and write the sentences. 
To the other rows in turn are assigned the other words, 
with the same directions, until the pupils have heard all the 
words used many times. If there are more than five rows of 
pupils, any of the words may be given a second time. Then 
the sentences are read and criticized — but not bv the teacher 



48 PEDAGOGICS OF GRAMMAR. § :^ 

until after the pupils have been heard and have critieized 
one another's work. This exercise may be extended to 
include, in one sentence, f7i'o of the given words, or a// of 
them in two or more sentences relating- to the same subject. 
In the Friday review the pupils may be required to write a 
brief essay on a subject assigned by the teacher or chosen by 
the pupil, and to introduce into it all the words studied dur- 
ing the week, underscoring them. 

If this work is faithfully done and properly reviewed, there 
is no better means of having children get a knowledge of the 
exact meaning of words, and of how to use them. 

The words assigned should, of course, be useful in every- 
body's vocabulary. 

Another synthetic exercise of somewhat greater difficulty 
is to reproduce orally, and later in writing, the reading lesson, 
or something read by the teacher. To tell in prose the story 
of a narrative poem, or of one that is descriptive, is also an 
excellent exercise. Such a poem as Eugene Field's exquisite 
"Little Boy Blue," or many of the poems in Robert Louis 
Stevenson's "Child's Garden of Verses" are suitable for this 
exercise. Many others that are usable for this purpose might 
be mentioned, such as Cowper's "An Adjudged Case," and 
others of his poems, Leigh Hunt's " Abou ben Adhem," 
Wordsworth's "We Are Seven," and innumerable other 
poems that will readily suggest themselves. Besides, there 
are many waifs that float about in the papers and magazines, 
which tho teacher can cut out and paste in a "Language 
Note Book. " 

40. " Sentence Bnilcling:.''' — The exercise known as 
^'■sentence building'' is another example of synthesis. It 
consists in the pupil's supplying and properly placing- one or 
more indicated sentential elements. 

Thus, the teacher may supply : 

1. A list of subjects, and require the pupil to find appro- 
priate predicates; and the reverse. 

2. A subject and a predicate, and require an attribute, 
an object, or a predicate noun. 



§ 3 PEDAGOGICvS OF GRAMMAR. 49 

3. A subject modified or unmodified, and require a variety 
of modified or unmodified predicates. 

4. A single word subject and predicate, and require the 
addition to each of several modifiers, one at a time. 

5. A list of subjects modified or unmodified, and a list of 
suitable predicates disarranged with respect to the subjects, 
and separated from them by a vertical line. Here the pupil 
is required to tmite subjects with suitable predicates. 

6. The same exercise as 5, with object, attribute, or predi- 
cate noun added. 

41. Anotlier Kxercise in Synthesis. — A very interest- 
ing exercise in synthesis — one that pupils enjoy very much — ■ 
is to restore to the best possible order the disarranged ele- 
ments of sentences. This closely resembles the exercise 
already described, which is suggested by the game of " Dis- 
sected Pictures." The teacher may write on the board or 
dictate the disarranged elements of any good sentence — its 
important words and its phrases — and require the pupils to 
embody them all in a written sentence as free from faults 
as possible. A few examples will illustrate. Suppose that 
the following fragments of a sentence are dictated to the 
pupils, and that they are to arrange them so as best to 
express the hinted thought : 

are dressed, of the year, in colors, iit the fall, the most beautiful, 
everywhere, the woods. 

Some such results as the following may be expected: 

" Everywhere in the fall of the year the woods are dressed in colors 
the most beautiful." 

"The woods everywhere are dressed in the fall of the year in colors 
the most beautiful." 

"In the fall of the year the woods are everywhere dressed in the 
most beautiful colors." 

" The woods in the fall of the year are dressed in the most beautiful 
colors everywhere." 

Many other arrangements are possible, and the very 
instructive matter for the pupils to consider is which 
arrangement is the best and the reasons why it is the best. 



50 PEDAGOGICS OF GRAMMAR. § 3 

The difficulty of the exercise may be increased or diminished 
by using long or short sentences. Simple and familiar 
poems may be thus dissected by the teacher and restored by 
the pupils. The exercise that follows will make the student 
familiar with the details. 

43. Exercise. — Arrange each of the following in a good sen- 
tence : 

1. a few, for the dismission, the signal, of school, in minutes, usual, 
will be given, without doul:)t. 

2. out of them, the child, yellow, to get gold, poor, for her mother, 
simple, buttercups, beloved, boiled. 

3. down the middle, there, a little girl, that hung, of her forehead, 
a little curl, was, who had. 

4. of the village, the rain, the mist, and, and, a feeling of sadness, 
see, comes, gleam, my soul, resist, through, cannot, I, the lights, o'er 
me, that. 

5. in shallow water, into the small streams, of the year, up the 
riv-ers, of fish, go, many kinds, to lay, in the spring, their eggs. 

43. The Iniprovement of Method. — The exercises 
above will indicate what is meant by sentence building, and 
the teacher fertile in devices will invent many more to 
emphasize the particular phase of the subject imder consid- 
eration. Such of these devices as are found to have good 
working value should be carefully preserved for future use. 
The teacher that means to grow in his profession must not 
be content to do his work in the same way year after year, 
using the same material. That is to get into a rut, than 
which nothing can be worse. What he has should serve to 
suggest something new and better, or at least improvements 
upon the old devices. He should realize that no life is long 
enough to reach the goal of perfect teaching. Each year 
should reveal imperfections in the work and methods of the 
last. The last stanza of Oliver Wendell Holmes' ' ' Chambered 
Nautilus" should serve as an inspiration to the teacher not 
only in mental and spiritual, but also in professional, growth. 
We make no apology for quoting it here, for nothing more 
noble, inspiring, and intrinsically beautiful was ever 
written. 



§ 3 PEDAGOGICS OF GRAMMAR. 51 

" Build thee more stately mansions, O, my soul, 

As the swift seasons roll! 

Leave thy low-vaulted past ! 
Let each new temple, nobler than the last, 
Shut thee from heaven with a dome more vast, 

Till thou at length art free. 

Leaving thine outgrown cell by life's unresting sea." 

44. Order of Sentential Elements. — In the construc- 
tion of a sentence the main object to be attained is such an 
arrangement of its elements as shall occasion the least possi- 
ble mental effort in understanding the meaning. The great 
masters in the art of composition have accomplished this, 
and hence the pleasure we find in reading their works. For 
the mind to build up, all in perfect logical sequence, the 
thought expressed by sentential elements, produces an emo- 
tion of pleasure; but, when the arrangement is illogical and 
out of sequence, a sense of confusion results, and, in conse- 
quence, pain. In most sentences, notably in long and com- 
plicated ones, a great variety of arrangement of the elements 
is possible. Obviously, there must be one arrangement 
easier of comprehension and more forcible than any other. 
Moreover, there must be some general principles dominating 
the order of elements. The importance of this subject to 
the teacher is very great. Professor Bain insists that, in the 
teaching of English, no exercise is so valuable as training the 
pupils in discriminating various arrangements with respect 
to their force, smoothness, clearness, and intelligibility. 

Mr. Herbert Spencer, in his "Philosophy of Style," intro- 
duces this general subject by discussing the question : Which 
is the better order, the French //// cJicval noir, '*a horse 
black," or the English, a black horse? In the former, upon 
hearing //;/ clicval, the mind instantly calls up the picture of 
a horse, — preferably the horse we drive daily, or see often- 
est, — it may be a white, a bay, a sorrel, or a chestnut horse. 
When the adjective noir follows, the mind is taken aback ; it 
must divest itself of the picture already formed, and substitute 
another. This involves the useless expenditure of mental 
effort, and is attended by a sense of bafflement that obscures 



52 PEDAGOGICvS OF GRAMMAR. § 3 

the image and unfits the mind somewhat for the confident 
interpretation of what may follow. The conclusion of Mr. 
Spencer's reasoning is that /// general a modifier should pre- 
cede the eleuient modified. So that, the adjective should pre- 
cede the element it modifies. Thus, 

" Great is Diana of the Ephesians." 

And Tennyson, 

" . . . . bright, and fierce, and fickle is the South, 
And dark, and true, and tender is the North." 

"And brief the sun of summer in the North, 
And brief the moon of beauty in the South." 

By inverting these extracts, much of their force and beauty 
is lost. Thus, 

" Diana of the Epliesians is great." 

" The South is bright, and fierce, and fickle,*' etc. 

Again, 

" Dctxr as remember'd kisses after death, 
And sweet as those by hopeless fancy feign' d 
On lips that are for others ; deep as love. 
Deep as first love, and 71.'//^/ with all regret; 
O Death in Life, the days that are n^) more." 

Here, the beauty of the whole is much enhanced by the 
precedence of the italicized adjectives which all modify days 
at the end of the stanza. 

45. Coinnion Usage. — Usage, however, requires that, in 
ordinary prose, and in the conversational style, the predicate 
adjective and the predicate noun shall follow the subject. 

Thus, we say, "The sky is red," not, "Red is the sky"; 
and " He is a gentleman," not, " A gentleman is he." Yet 
we believe that any one can feel the superior force of the 
second forms. 

In like manner the most forcible position of the adverb is 
before the element it modifies. Thus, " Blandly and sweetly 
he smiled." — " He smiled blandly and sweetly." The former 
is clearly the more forcible, but it is the poetical, not the 
prose, arrangement. 



§ 3 PEDAGOGICS OF GRAMMAR. 53 

" the gods, who haunt 

Tlic lucid interspace of world and world, 
Where nc7>er creeps a cloud, or moves a wind, 
Nor ever falls the least white star of snow. 
Nor ever lowest roll of thunder moans, 
Nor sound of human sorrow mounts to mar 
Their sacred, everlasting calm." 

In the above quotation, not only do the adverbs precede 
the elements they modify, but the subjects cloud, %vi>id, and 
star follow their verbs — this being their poetic and most 
forcible order. 

" And siueet it was to dream of Fatherland, 
Of child, and wife, and slave; but evermore 
Most weary seem'd the sea, weary the oar. 
Weary the wandering fields of barren foam." 

In this quotation will be seen the same arrangement of 
predicate adjective and verb, and of subject and predicate. 

It is, however, in the formation of compound words that 
we see best exemplified this law of arrangement. Sidcivalk, 
steamboat, zuatfr-whecl, ivatcJi-kcy, douni-Jicartcd, short- 
sighted, trolley-car, overcoat, are examples. Indeed, it would 
be difficult to find a compound word in which the modified 
part is not placed last. 

46. The General Law of Sequence. — Briefly stated, 
the law of sequence, not only in the structure of compound 
words, but also in sentential structure, is from the abstract 
to the concrete — from the less specific to the more spec fie. 

If a complicated sentence contains many phrases and 
clauses that modify, and to carry them all in the mind and 
hold them in readiness for the main idea becomes burden- 
some, a judicious distribution of them is often better. Mr. 
Spencer gives the following as an example; first, with the 
modifiers of the predicate placed after it: 

"We came to our journey's end, at last, with no small difficulty, 
after much fatigue, through deep roads, and bad weather." 

He qtiotes from Dr. Whately the following arrangement: 

"At last, after mrich fatigue, through deep roads and bad weather, 
we came, with no small difficulty, to our journey's end." 



54 PEDAGOGICS OF GRAMMAR. § 3 

Mr. Spencer suggests as better: 

"At last, with no small difficulty, and after much fatigue, we came, 
through deep roads and bad weather, to our journey's end." 

Of these arrangements it may be observed that the first is 
extremely awkward and entirely inadmissible. It illustrates 
very forcibly the weakness that results from putting modifiers 
last. The second arrangement is better, but its modifiers do 
not proceed from the less specific to the more specific. J/7/// 
no small difficulty is less specific — less concrete — than any 
preceding phrase except <-?/ A?^/. In Mr. vSpencer's rearrange- 
ment, the modifiers are in the order of increasing concrete- 
ness, and, besides, they are placed before and after the 
predicate verb came in such proportion as to make the mental 
effort in grasping the thought the least possible. The mod- 
ifiers that follow the verb do not materially change the 
meaning of the whole, and their effect is easily added. 

It appears, therefore, that while, in general, modifiers 
should precede the terms they modify, the task of carrying 
in the mind conditioning elements may become so great that 
a judicious distribution of them, such as is indicated in the 
above sentence, becomes necessary. The fact is that it is 
only the most vigorous mind that can vividly retain the 
modifying effect of many phrases. and clauses, and apply 
them with their full force to the modified part. For ordi- 
nary minds, it is better to distribute the modifiers, placing 
some before, and some after, the main statement. In doing 
this, care should be taken to arrange them in accordance 
with the law already indicated: To produce the greatest pos- 
sible mental effect, modifiers should proceed in order from the 
abstract to the concrete, from the less specif c to the more spe- 
cific, and, if numerous, they should be placed, some before 
and some after, the predicate. 

47. Syntliesis of Complex Sentences. — In complex 
sentences the subordinate clause should, in general, precede 
the principal clause; but when there are two .subordinate 
clauses, it may be better to place one of them, usually, the 
more specific, after the main clause. 



§ 3 PEDAGOGICS OF GRAMMAR. 55 

" When the tide turns we shall set sail." 
" If you wish to govern wisely, learn to govern yourself." 
" If I mistake not, I met him when we made the charge at Gettys- 
burg." 

In this .sentence, If I mistake not is less specific than 
ivJien wc, etc., and the arrangement is better than to 
put both subordinate clauses before the principal clause. 
Of the six possible arrang-ements of the three clauses 
in the sentence above, the order given is undoubtedly the 
best. 

Even in poetry and highly emotional prose, the principle 
of tJic least mental resista)iee may make necessary a sequence 
of sentential elements different from that dictated by theory. 
In other words, there is in language work no exercise requir- 
ing better judgment and nicer discrimination than the dis- 
position of the words, phrases, and clauses that make up a 
complicated sentence. Moreover, no exercise yields better 
resitlts than that so much insisted upon by Mr. Bain — trying 
the ear and the mind upon all possible arrangements of a 
sentence, the end in view being to determine which is mo.st 
forcible, clear, smooth, and easy of comprehension. The 
ultimate object of such exercises is the acquirement of a 
taste — an automatic mental action that shall at once select 
the best sequence of sentential elements. As soon, therefore, 
as the mental maturity of the pupil is sufficient for the 
exercise, the teacher should, during the reading lesson, 
start questions as to the best possible sentential arrange- 
ment. He will find his reading book full of faulty sentences 
that even comparatively young children can rearrange and 
improve. Clauses may often be condensed into phrases, or 
even into single words. On the principle that force is gained 
by brevity, this will generally be a means of bettering the 
sentence. The exercise of expanding words into phrases 
and clauses, and phrases into clauses, is almost equally 
valuable; for in the manipulation of language it furnishes 
much needed skill, and is perhaps the best method of enlar- 
ging the pupil's vocabulary, and of rendering more precise 
his notion of the meaning of words. 



50 



PEDAGOGICS OF GRAMMAR. 



SUMMARY. 

48. Tabular Classification of Heiiteiices. — The fore- 
going general treatment of the sentence would be incom- 
plete without a synoptical classification as to form and use. 
The writer believes that the following tabular view will be 
found by the teacher to be helpful: 

r 1'. Exclamatory- 
"] I declarative. 

I + strong ) _ J 2'. Exclamatory- 
emotion f interrogative. 
3'. Exclamatory- 
imperative. 



'A 



As to 

Use 



1. Declarative 

2. Interrogative 
I 3. Imperative 



1. vSimple 



r Subject and Predicate Simple. 

j .Subject Compound, Prediciite Simple. 

I Subject Simple, Predicate Compound. 

1 

[ Subject and Predicate Compound. 

f One Principal, one Subordinate Clause. 
As to ^^ _, I ^ 

Form > ''^' ^*^™Pl^^ ^ One Principal Clause, two or more Sub- 

[ ordinate Clauses. 

( Two Coordinate Clauses. 

Two Principal Clauses, one or more Sub- 
^ 3. Compound J ordinate Clauses. 

More than two Principal Clauses, one or 
more Subordinate Clauses. 



49. Remarks on the Table. — The teacher must not 
assume that every possible variety of .sentence is included in 
the six forms that, in the table, are classified with respect 
to use. A declarative clause may be combined with an 
interrogative clause to form a complex or a compound sen- 
tence. In like manner, a declarative clause may be united 
with an imperative clause. Moreover, either combination 
may be exclamatory, and either may be accompanied by 
clause modifiers. Many other varieties of union are pos- 
sible. In classifying such sentences, the character of the 



§ 3 PEDAGOGICS OF GRAMMAR. 57 

successive clauses should determine the order of the terms 
indicating the classification. Some illustrations follow: 

A Coiiipouiid Impcrativc-Dcclarativc-Exclamatory Sen- 
tence: 

" Stand ! the ground's your own, my braves ! " 

" Come one, come all; this rock shall fly 
Fi'om its firm base as soon as I ! " 

A Complex Imperative- Deelarative-Exelainatory Sentence : 

" Flee, if you value your lives 1 " 

A Compound Deeletrat ive- Lit errogat ive Sentence : 

" Death is the end of life; then \\\\\ should life all labor be?" 

50. Couuectives in the Classification of Sentences. 

The presence of a connective between clauses is not neces- 
sary to indicate that they are to be taken together. Indeed, 
where the element of strong emotion enters, connectives are 
usually omitted. Their absence denotes incntal turmoil and 
excitement; their presence, repose and mental balance. The 
degree of connection must be determined from the context 
and from the meaning. 

51. Pnnctnation in tlie Classification of Sentences. 

Neither should the punctuation determine whether the 
clauses are to be taken separately, as sentences, or together, 
as parts of a compound or a complex sentence. Few teach- 
ers, for example, would hesitate about treating the following 
stanza, however it might be pimctuated, as one compound 

sentence : 

" Woodman, spare that tree! 

Touch not a single bough ! 

In youth it sheltered me, 

And I'll protect it now." 

Here, again, is an opportimity for the discipline of the 
judginent and the powers of discrimination; for it would be 
almost impossible to find tw^o writers that would punctuate 
in the same way a long, complicated paragraph, to say 
nothing of a poem, a letter, or a magazine article. As has 
been said, most authors pimctuate their composition in 
accordance with their notion of the manner in which it 



58 PEDAGOGICS OF GRAMMAR. § 3 

should be read ; but, since an author is likely to feel more 
strongly than others the meaning he intends, it follows that 
his punctuation will differ from that of his reader, who is 
not influenced by the "white heat of composition." Again, 
it would be difticult to find two readers of an emotional pas- 
sage whose conceptions of its rendition would agree. No 
two actors have ever rendered Hamlet in the same manner; 
the words they used were the same, but the pauses, the 
inflections, the gestures, were different. 

The teacher, therefore, in determining the closeness in the 
sequence of the elements of a paragraph must be guided, 
not by the punctuation alone, but also by the degree of 
earnestness intended to be expressed, by the emphasis used 
in reading it, by the length of the elements themselves, 
and by many other considerations. 



SPECIAL COIS^STRUCTIOXS. 

53. Pleonasm. — In classifying sentences, the teacher 
will frequently meet a very puzzling construction that gram- 
marians have called pleonasm. The word is derived from 
the Greek v^ord p Icon, more. It signifies the employment of 
more words to express a thought than are really necessary. 
The term tautology is often used in much the same sense; 
but pleonasm is the generic term of which tautology, rediin- 
daney, prolixitxy, and verbosity are species. The treatment of 
this subject properly belongs to rhetoric, but its importance 
in the classification of sentences is the writer's excuse for 
briefly referring to it in this place, and exemplifying it. 

Tyndall, in one of his books, quotes the following passage, 
saying of it that a subject seems to be "left floating in the 
air. " 

" He that hath ears to hear, let him hear." 

The subject meant is lu\ which has no accompanying verb. 
That hath ears to hear modifies both he and Jiim. The Jie is 
superfluous; for, rearranging the sentence, we have, Let him 
hear that hath ears to hear. He, in this case, is said to be 



§ 3 PEDAGOGICS OF GRAMMAR. 59 

"in the nominative case by pleonasm." The construction 
is a very common one, and is frequently found in the best 
authors. 

" The boy, O, where was he ?" 

"The sweet babe," said the king, "she shall be cared for by the 
queen herself." 

" A human cry; methought I heard a human cry." 

The effect of simply moitioiiiiig the matter that is to be 
the principal content of a sentence to follow is to concen- 
trate the attention upon that idea. It is an effective rhetor- 
ical device. 

Perhaps to suggest, by means of an elliptical question, the 
subject matter of a following sentence should be regarded as 
another form of pleonasm. 

" The woman's cause? The woman's cause is man's; they rise or 
fall together." 

"A healthy body? It is an indispensable condition to a healthy 
mind." 

" The sea ? God bless us ! The sea ? It is the greatest thing God 
ever made." 

It is a cjuestion whether, in the last sentence, everything 
as far as // were not better treated as independent by pleo- 
nasm. It is certain that there is no grammatical relation 
between the sentence and the exclamatory matter; yet the 
latter cannot be regarded as composed entirely of interjec- 
tional matter. 

Sentences preceded by such matter, therefore, should be 
classified as if they stood alone. The effort to fill up the 
supposed ellipses simply results in changing the meaning of 
the whole, and in spoiling the rhetorical effect. The point 
aimed at in our system of diagrams is to avoid the dismem- 
berment of sentences. They should be taken with the idioms 
they contain, withoitt supplying ellipses never contemplated 
by the author. 

53. Otlier Forms of Pleonasm. — There are other varie- 
ties of pleonasm, such as saying the same thing more than 
once in the body of a sentence ; as, " He told me the very, 



(iU PEDAGOGICS OF GRAMxMAR. § 3 

identical, same thing," for "He told me the same thing." 
This is usually called tautology or redundancy. 

If an idea differently expressed is repeated in two or more 
successive sentences, or in two or more clauses of a sentence, 
it is a form of pleonasm called //W/>//j/. But the only variety 
that needs to be noted here is the one explained above, where 
the pleonasin consists simply in mentioning the subject 
matter of a sentence to follow. This is good, strong, 
idiomatic English; the other forms are always blemishes, 
and should be carefully avoided. 



FALSE SYNTAX. 

54. Error as Example. — Some of our educators insist 
that, so far as the teacher can accomplish it, error of every 
kind should be kept from the mind of the pupil. He should 
never be permitted to see or to hear a word wrongly spelled, 
lest, later, it might displace in his mind the correct form. 
These educators say also that the pupil should never be 
required to rectify errors in grammar, but should be exer- 
cised solely in classically correct English. In reply to all 
this it may be said that the pupil hears bad English con- 
stantly. The air is full of it. If he goes out to play, he 
hears it from his playmates ; if he goes to school, he hears it 
from his classmates — and from his teacher. He hears it in 
nine out of ten of our homes ; he meets it in the books he 
reads and in the grammar he studies. Who, indeed, always 
speaks correctly ? Not the teacher, the school principal, or 
the school superintendent ; not the minister, not the lawyer. 
It is granted that a very few people blunder but rarely, but 
the number of such is not one-tenth of one per cent, of our 
population ; and there is perhaps no one that a/ways speaks 
classically pure and otherwise correct English. It is doubt- 
ful whether any one can be found that invariably writes so 
as to be above fair criticism. Only today one of my children 
came home from the High School and told of an impressive 
lecture upon the beauty and importance of speaking good 
English. This was followed by the question, " Now is there 



§ 3 PEDAGOGICS OF GRAMMAR. 61 

anythin^^- in this lesson that anybody don't understand ?" It 
is generally assumed that in conversation a certain margin of 
incorrect speech should be allowed, even to teachers, on the 
same principle that a moderate license is granted to poets. 
If it is human to err, it would seem to follow that to be 
always right should be accepted as evidence of divinity. 

The reasoning of those educators that would keep from the 
pupil all incorrect forms would prevent us from indicating 
the meaning of a word by giving an approximate synonym, 
for the authorities tell us that no two words of exactly the 
same meaning can be found. To the writer this contention 
seems utterly indefensible. We learn perhaps more from bad 
example than from good — more from unlikeness than from 
likeness. Nothing is qiiite .so emphatic as contrast. 

55. Some Illustrations. — False syntax, therefore, is 
proper matter upon which to exerci.se the judgments of our 
pupils. The likelihood of their retaining the incorrect form 
and of confusing it with the correct, is purely imaginary. 
As long as we hear cultivated people saying " I feel badly," 
" vShe looks nicely," "prettily," etc., exercises in the correc- 
tion of false syntax seem to be, in ohr schemes of education, 
very much in order. The writer, not long ago, overheard 
the superintendent of schools of one of the largest cities in 
the United States answer the questions of a friend: " How 
are you today?" "Nicely, thank you." "And Mrs. — — , 
is she well?" "No; she complained of feeling badly this 
morning. " 

The writer was asked a short time ago whether one should 
say "The package arrived safe,'' or "The package arrived 
safely. " The inquiry was made by a gentleman that has 
for many years been a writer of books, and yet he had not 
learned to discriminate betw^een the case where the action 
expressed by the verb is to be modified by an adverb and that 
where the state of the subject is modified by a predicate 
adjective. In this example, a little reflection makes evident 
that it is not the act of arriving that is safely performed, 
but that it is the state or condition of the package after the 



62 PEDAGOGICS OF GRAMMAR. § 3 

act is finished. The package is safe after the act of arriving 
is complete. 

There is a long list of what soiPie grammarians call neuter 
verbs that must be followed by adjectives expressing a state 
or condition of the subject. Some of them are the forms be, 
seem, feel, appear, get, beeome, look, etc. Besides these, 
innumerable active verbs are used in the same way. 

Ope?i your eyes tvide. Shut the door tight. The general 
sat erect upon his horse. Do not aet silly. Sometimes it is 
difficult to tell whether it is the meaning of the verb or of 
the subject that should be modified. But, if the adjective is 
used, it is the subject to which the attention is directed ; if the 
adverb, we must think of the action expressed by the verb. 

" The citizens stood firm for their rights." 
"The citizens stood firmly for their rights." 
" Quick as a flash the man sprang to his feet." 
"The man quickly sprang to his feet." 

This subject will be treated more fully in another place. 
It has been introduced here only as an illustration of the 
need for exercises in correcting false syntax. 

56. Collections . for Correction. — The teacher should 
be provided with a note book in which should be arranged a 
well classified list — 

1. Of local errors in speech — those frequently heard in 
the neighborhood where he teaches. 

The writer knows of a large city in this country where the 
expressions "quite some," "quite a few," and "quite a 
little " are imiversally current. Even the clergymen of 
the city use them in the pulpits, and nobody seems to know 
that they are gross errors of speech. In a conversation with 
one of the clergymen of the place, the writer mentioned the 
fact that these errors were in general use in the city. " I 
think that I do not use them," he said. "Constantly; yon 
use them constantly, " was the answer. "I really did not 
kriow it, and I shall try to avoid them in fttture." But he 
continued to say "quite some," and, if he is still alive, he 
probably commits the same blunder. 



§ 3 PEDAGOGICS OF GRAMMAR. G3 

2. Of errors that ma}- be heard elsewhere, or found in 
books, ma^'azines, and newspapers. 

In the course of a few terms, a large variety of examples 
illustrating errors can be accumulated, even if they are 
sought for in our best authors. 

The object to be attained is, primarily, to exercise and 
sharpen in the pupil the power of discrimination, and, 
secondarily, to make him careful of his own speech. If the 
teacher expects to add materially to the correctness with 
which his pupils speak the mother tongue, he will be disap- 
pointed. It is only when we have learned the difficult art of 
listening critically to onr ozvn language Wxa.X. rapid improve- 
ment in speech begins. This is almost as difficult as the 
task the stenographer must master — -that of writing one sen- 
tence and of accurately hearing and remembering the next. 

In the correction of false syntax, after the teacher and 
pupils have gone over the examples orally, and have dis- 
cussed the principles involved, the corrections should be 
made in writing, with or without reasons, as the teacher may 
direct. This work should be done, not on slates, but on 
paper; it is good practice in composition. 



ACQI IRIXC; A TOCAIil LARY. 

57. Tlie ?^atiii"e of our KuoAvletlge of Words. — 

Every person knows the meaning of hundreds, perhaps 
thousands, of words he never uses. His failure to use known 
words does not come from the fact that they are iiseless and 
would not embellish his speech. Indeed, the best measure of 
a man's culture is the abundance and variety of his stock of 
words, and the precision and discrimination with which he 
uses them. A large vocabulary is, therefore, something 
worth laboring to acquire. But why, when we know the 
exact meaning of a term, is it not ours for daily use ever 
afterward? Oliver Wendell Holmes says: "My thoughts 
flow in layers, or strata, at least three deep. I follow a 
slow person's thought, and keep a perfectly clear undercur- 
rent of my own beneath it. Under both runs obscurely a 



64 PEDAGOGICS OF GRAMMAR. § 3 

consciousness belonging to a third train of reflections, inde- 
pendent of the other two." 

Sometliing akin to this is true of the words we know. 
They are in layers. The top layer consists of the words we 
learned in childhood, increased by a slow accumulation since. 
These words call up the most vivid images that the mind is 
capable of forming. It is our ordinary, daily, working vocab- 
ulary. We use it in our home conversations, wath wife and 
children, and with our oldest and dearest friends. 

In society, with those whose life environment has been 
different from our own, we draw largely from a second 
stratum of words, using at the same time many from the 
first layer. But here our conversation fakes on a certain 
hesitancy and artificiality not found in our familiar talk at 
home. We are conscious of a want of promptness in the 
words getting into proper place and relation in our sen- 
tences. The home talk is almost perfectl}^ automatic; this 
costs us an effort, and is, therefore, less pleasurable and 
much less forcible. And so, all the world is agreed that 
"old friends are best," and this arises partly from the fact 
that they have many memories in common with us, and 
partly because they use, in the main, the same vocabulary 
that we use; it is easier to converse with them. 

Lower still is a stratum containing many technical terms, 
and Latin and Greek derivatives. In our miscellaneous 
reading we have met these words once or twice a year for 
many years, until we know from the various contexts, 
or from the dictionary, exactly, or nearly, what they mean. 
But as the memory is called upon for words in which to 
express our thought, these words show no tendency to take 
their places in our sentences. Rarely, one of them will, so to 
speak, stir or turn over, indicating that an impulse was felt, 
but it was not strong enough to dislodge it from its place. 

58. Method of Ijearning Words. — But, how do new 
words get into our working vocabulary ? The primary con- 
dition is, that we shall hear them daily and for a considera- 
ble time. It is reiteration — repetition — that does it. Years 



§ 3 PEDAGOGICS OF GRAMMAR. 65 

ago I stopped for a time in a family where the word appre- 
hend was constantly used. It was a synonym for thifik, sup- 
pose, believe, imagine, fear, conjecture, and many other words. 
Of course, I noticed the excessive use of the word, and I 
noticed, too, that the wife and a son and daughter employed 
the term with almost the same frequency as the father. I 
observed later that the w^ord began to offer its services in 
my own sentences — an offer that I steadily declined. But 
even to this day the word will come and cause me a momen- 
tary delay in finding a substitute. 

This necessity for reiteration, repetition, review, is the 
one indispensable condition of success, not only in making 
permanent and useful additions to the pupil's vocabulary, 
but also in giving him a firm, lasting, and usable hold upon, 
anything that he studies. Teachers constantly complain of 
the fact that their pupils forget so soon the things that have 
been so carefully taught. Reviews, and more reviews — that 
is the remedy. The brain tissue of growing children changes 
rapidly, and old things pass away or fade into a general con- 
fusion of images. They must be renewed again and again. 

59. Getting- Rid of Objectionable Words. — The cor- 
rectness of the method of acquiring words as described above 
is confirmed by the experience we find in the effort to get rid 
of an objectionable word. Have you, my reader, managed to 
get the word nice into your vocabulary ? Do you say, ' ' It was 
a nice speech," "a ///rt'day," '^ nice soup," "■nice sleighing," 
" nice singing, " " a nice house " ? Is she a nice lady on a nice 
horse riding along a nice road to a nice town in the distance, 
where there is a nice store, full of nice attendants, that will 
sell her all manner of nice things ? Try to expunge the 
word from your vocabulary, and learn to use terms that dis- 
criminate these many different nice things. You will find 
that the word is in the upper layer, zealous to be serviceable 
as a sign of the absence of mental activity. It is a tenant 
having a lease in perpetiiity, who refuses to be dispossessed. 
Without knowing that you have used the word, you find it 
in your sentences, its presence demonstrating the tyranny of 



6Q PEDAGOGICS OF GRAMMAR. § 3 

habit. Even if you do learn practically to construct your 
sentences before you speak them, the task of finding a sub- 
stitute for the offensive little intruder is so onerous that you 
give up the struggle from sheer weariness. We are reminded 
by all this of the comment that Cassius makes on Brutus 
after he had consented to join the conspiracy against Csesar. 

"Well, Brutus, thou art noble; yet, I see, 
Thy honorable metal may be wrought 
From that it is disposed; therefore 'tis meet 
That noble minds keep ever with their likes; 
For who .so firm that cannot be seduced ?" 

A new word that every person should avoid seems to gain 
a wide currency Avith a facility and rapidity that no word of 
good lineage can show; and the difficulty of getting rid 
of a word appears' to become greater as its offensiveness 
increases. 

60. Enlarg'ing the Pupils' Vocabularies. — It is 

clear, then, that if the teacher would enlarge the vocabulary 
of his pupils, he must expect to do it slowly. Twenty new 
words per week have been suggested in a former paragraph 
as a sufficient number. It may be added here that the teacher 
actually able to put so many good and useful words weekly 
into the working vocabulary of his pupils, — into the " outer 
layer,'' where their response to the mind's demand for signs 
for its thought is automatic, — mitst be an artist in the teach- 
ing of language. Yet this is the goal for which he should 
strive. Words that we know but do not use, have a value in 
enabling us to imderstand what we hear or read ; but only 
when we use them without conscious effort, do they change 
our personality and transform us before the world. It should 
be observed that learned, technical, and pedantic terms, even 
if they respond promptly to the mind's call for words, should 
be avoided in ordinary conversation. The reasons for this 
avoidance are so obvious as to require no statement. 

61. General Remarks. — In the preceding pages the 
sentence has been taken as the "ttnit of thought," and stich 
general considerations have been discussed as it was believed 



§ 3 PEDAGOGICS OF GRAMMAR. 67 

would be helpful to teaehers of language and grammar. 
No attempt was made, however, to suggest an orderly 
method of procedure in teaching these subjects. That will 
be found in any good modern textbook. 

We come now to a treatment of U'onh. Just as the unit 
of thought is the sentence, so the sentence unit is the word. 
The sentence is here treated before any attention is given to 
the words that compose it. This is in accordance with the 
opinions of our best authorities on education, and it is in the 
same order as the development of speech. As we learn to 
recognize faces before we notice attentively the features that 
make them up, so the child learns to express his thought in 
sentences, giving no special attention to the words of which 
they are composed. It is impossible, however, entirely to 
separate syntax from etymology, and in what follows no 
effort shall be made to do so. 

The treatment of the sentence, so far, is of the wider kind 
that includes not so much what the teacher must introduce 
among the things he teaches, as matters that every teacher of 
language should know and think about. No one is competent 
to teach a subject familiar to him no further than he is 
required to teach it. Every teacher should have a large 
fund of general information, and besides, he should know 
very thoroughly, at least all the subjects he is required to 
teach; or, as some one has said, "The teacher should know 
something of everything and everything of something. ' 



ETYMOLOGY ^JST> SYNTAX. 



PRELIMINARV REMARKS. 

'^ ^. IMeaning' of TCtyniolo^^'y, — The word etymology is 

I i" e 1 from the Greek w^ords t:TVjiog, ctymos^ "real," 

"sure," "true," and "koyoc, logos, "aword, " " a discourse. " 

P-imarily, therefore, it should treat of the triic meaning 

of words as determined by their histor}^ derivation, and 



68 PEDAGOGICS OF GRAMMAR. § 3 

inflection. Thus, from love we have loved, 'lover, loves, loving, 
lovely, etc. These variations of form are for the sake of 
denoting" that the root idea in the word love is to be conceived 
of under various conditions of time, niiiiibei', action, etc. As 
a purely grammatical term, the word etymology, in its modern 
use and sense, means, " The branch of grammar that treats 
of the parts of speech and their inflections; the science of the 
elements of the sentence." It is with this meaning that the 
term is here used. Although the study of the origin and the 
history of words — etymology in its literal sense — is very 
fascinating and profitable, and a study that the teacher can 
scarcely afl'ord to neglect, yet the task of teaching it to 
immature pupils is one that yields but a poor return for the 
labor involved. It is rather a subject for the scholar in his 
library. It is conceded, however, that in the later stages of 
grammar work, the study of prefixes and suffixes can be 
made a source of much profit and interest to the pupil. But, 
in view of the inultitude of subjects that have a direct and 
vital bearing upon the questions of success in life and of 
human progress, we are not wise to consume our time in the 
study of a subject for no better reason than that it is interest- 
ing, and, to a degree, profitable. More and more, educators, 
in arranging the subject matter in which our children are to 
be educated, are taking into accoimt the probable life environ- 
ment of those children. How should they be trained so as to 
be fitted to do life's work most effectively for their own advan- 
tage and in the interest of the progress of the race ? That 
is the crucial question for the teacher and the educator. We 
must not, in this life so full of needs to be satis'fied — physical 
as well as aesthetical and spiritual — allow ourselves to be the- 
orized into an educational Utopia. We owe something — much 
more indeed than is generally suspected — to the house we live 
in — the body. It must be fed and clothed, of course; but, 
besides this, the repose, comfort, and health of its tenant are 
worthy of the most careful attention and forethought. 

(>8. Method of Treatment. — Professor Bain and some 
others insist that the parts of speech should be taught before 



§ 3 PEDAGOGICvS OF GRAMMAR. 69 

their properties or inflections are taken up. There is good 
reason for this, for a child can learn to distinguish nouns, 
adjectives, verbs, etc. long before he can understand what is 
medinthy person, ease, degree, mode, or tense. There is, per- 
haps, equally good reason for departing from the usual order 
in which the parts of speech are presented in our textbooks. 
If the sentence is to be regarded as the "unit of thought," 
it is obvious that its elements — words — should be treated in 
the order of their relative importance in the sentence. 

64. Etymology and Syntax Sliould Be Treated 
Tog:etlier. — To study words as used in speech they must be 
treated with reference to their office in the sentence, and 
their relations there to one another. For it is only by these 
relations that we can tell an adjective from a noim, or a verb 
from a preposition or an adverb. It follows, therefore, that 
etymology and syntax ought not to be separated in the study 
of language, although imtil recently this has usually been 
done. In this work, the main concern with respect to any 
matter, will not be whether it is a question belonging to 
etymology or to syntax, but whether it belongs to the sub- 
ject of grammar and language. 

65. Comparative Importance of Sentential Ele- 
ments. — In the simple sentence, the subject noun or pro- 
noun, and the predicate verb are the centers about which 
everything else clusters. They are, besides, the easiest 
parts of speech to recognize. With these will follow, in 
logical order, the word modifiers of the subject — adjectives, 
nouns in the possessive case, and the various pronouns that 
modify — then word modifiers of the predicate verb ; and, 
finally, connectives, including prepositions, conjunctive 
adverbs, relative pronouns, and conjunctions proper. Then 
should follow complex and compound sentences with phrase 
and clause modifiers. 

After thus going over the parts of speech with the object of 
becoming familiar with their classification as determined by 
their use or function in sentence structure, their inflections 



70 PEDAGOGICS OF GRAMMAR. § 3 

may be studied. The interjection naturally belongs with 
the independent constructions, the nominative case abso- 
lute, by address, and by pleonasm. 

Peculiar and idiomatic constructions may receive separate 
treatment, or they may be taken in connection with the 
parts of speech to which they are most closely related. 

With reference to the order of treatment indicated above, 
it may be remarked that it is one specially suited to the 
graded schools of our cities, large towns, and villages. A 
teacher beginning the study of grammar and language in 
the higher primary grades will find Mr. Bain's suggestion, 
referred to above, a good one. In higher grades, when the 
subject is to be completed and reviewed, no harm can come 
from following the 'Latin and Greek order that most of our 
writers have copied. Still, logical arrangement and logical 
methods of procedure are always b^st. 

C6. Terms Used by AVriters on Oramniar. — Before 

beginning the treatment of the several parts of speech, it 
should be observed that in their treatment of etymology 
there is much diversit)^ among authors in the use of terms — 
a fact especially noticeable in the case of the- verb. These 
diversities will be noted in their proper places. 



THE IsOUX. 

G7. Introductory. — The word noun is derived through 
the French from the Latin nonien^ a name. A noim is, there- 
fore, a liavic of anything. Tins definition follows so natur- 
ally from the original term, and is so simple that one might 
easily infer that all grammarians would be content with it; 
but it will be shown in a later paragraph how our authors 
have endeavored to differ from one another in defining the 
term. 

68. Gradation of Treatment. — One of the errors most 
likely to be made by an inexperienced teacher is the failure 
to observe grades of difficulty in recognizing the noun, and to 



§3 



PEDAGOGICvS OF GRAMMAR. 



71 



arrange his work in accordance therewith. Nouns may be 
conveniently taught in four groups: 

1. Names of material objects denoted by single words; as, 
boy, horse, slate, book, etc. 

2. Names of immaterial objects denoted by single words ; 
as, thought, memory, wisdom, plan, etc. 

o. Names of material things denoted by several words; 
as, '^A piece of rock broken fr-om tJic mount aiii rolled down 
into the valley. " 

4. Names of immaterial things expressed by several 
words; as, "■ Livi)ig in a city is expensive." ^^The search 
for the north pole has not yet been successful. " 

It is extremely easy for the pupil to recognize nouns of the 
first class, and to be taught to put them into sentences as 
subjects, predicate norms, and as objects of verbs or of prepo- 
sitions. The special value of the norms included under 3 
and 4 is to teach that a noun, or substantive, does not neces- 
sarily consist of one word, and that it is use or function that 
determines etymological classification. After the pupil has 
clearly seen that a certain phrase or clause is used as a noun, 
he may be required, when the proper time arrives, to clas- 
sify its several components. 

09. The Noun Witli Modiflei's. — Before passing to the 
second class, the pupils should be trained in finding for a 
given noun all possible appropriate modifiers. The reverse 
exercise of finding a noun forgiven modifiers would naturally 
suggest itself to the teacher. In these exercises the brace 
should be constantly used. Devices like the following will 
be found useful: 



A 



obedient 
careless 
truthful 



An 



bov. 



A 

or 

An 



J 



pretty 
studious 
amiable 



1 



- girl. 



While in these exercises the pupil is required to find mod- 
ifiers for nouns, and nouns for modifiers, thus keeping up his 
acquaintance with word arrangement, he is not supposed as 



72 PEDAGOGICS OF GRAMMAR. § 3 

yet to know or use the word adjective. The term "modifier " 
which he employs, serves a better purpose, for it denotes 
fu7iction; adjective doe^ noi. The more familiar he becomes 
with the offices and relations of words in sentences, the more 
significant to him will be the etymological names when he 
finally reaches them. 

70. Other Matters Connected With the Study of 
the Noun. — The difference between the pronunciation of the 
before a consonant (thu) and that of the same word before a 
vowel (the) may be emphasized by suitable exercises, as may 
also the distinction in use between a and an. If handled 
properly, the utmost enthusiasm may be aroused in a class 
by such exercises, and many others may be invented by the 
teacher or found in our textbooks. Of course, the teacher 
will preserve in a note book such devices as are found good 
in practice. 

The choosing of suitable predicates for nouns used as sub- 
jects may be reviewed during the study of the noun. It is 
extremely important, too, that children should not be left in 
doubt as to whether it is the word or the tiling that is the 
noun. 

After a thorough drill with nouns denoting material 
things, nouns denoting iimnaterial things may be taken 
up and treated in the same way ; — a much more difficult 
exercise. The pupils may be asked to point out the nouns in 
their reading lesson, and to make sentences in which other 
parts of speech are, without change of form, used as nouns. 
vSuch words as zoalk, love, fire, stop, start, etc. are examples. 

Then should follow those substantives that are composed 
of several words — phrase and clause nouns. It will be noticed 
that these divisions of the noim are progressive in difficulty, 
the last being by much the most formidable. But, if each 
is thoroughly mastered before passing to the next, the work 
necessary will be reduced to a minimum. 

71. Definitions of the Xonn, — It might be assimied 
that in a matter so apparently simple as defining the noun, 
grainmarians would long ago have agreed. But such is not 



§ 3 PEDAGOGICS OF GRAMMAR. 73 

the case. Each author seems to regard it as imnerative that 
his definition shall b'e in some respect different from the 
definitions of his predecessors. The following will illustrate 
some of the variations: 

1. "A noun is the name of any person, place, or thing." 

2. "A noxm is the name of any person, place, or thing 
that can be known or mentioned." 

3. '.'A noun, or name word, is the name of anything 
existing or conceived by the mind." 

The author of 3 explains in a note the meaning of thing 
or anything : " The word 'thing,' or 'anything,' used in its 
widest sense, as above, signifies whatever we can tJiink about, 
and applies to persons as well as to inanimate objects." 

4. "A iioviii is a word used as the name of something." 

5. "A noun is the name of anything." 

6. "A nonn is a name, or any word or words used as a 
name. " 

7. "A noim is a word used as the name of a thing, 
quality, or action existing or conceived by the mind. " 

Of these definitions it may be observed that the longest 
seem to be least satisfactory, for the reason that their diffi- 
culty of being understood by the pupil increa.ses with their 
length. Moreover, a long definition is more liable to contain 
tautology than a short one. Thus, the author of 3 explains 
that thing or anything includes persons; hence, in 1 and 2 
the words person and p/acc are superfluous. In 3, the words 
existing or conceived by the viind add nothing to the thought. 
Besides, anything, either material or immaterial, that is 
conceived at all, is conceived by the mind. Definition 3, 
therefore, would be much better without the last six words. 
The same kind of objection may be made to 7. Definitions 
4 and 5 are, of all that are given above, least open to criti- 
cism, and, if the words or any word were omitted from 6, it 
would pei^haps be the best of all. 

A noun is a name, or laords used as a name. 

An obvious inference from all this, and one of special 
importance to the teacher, is: be brief — in your definitions, 
in your ordinary conversation, in your explanations and 



74 



PEDAGOGICS OF GRAMMAR. 



3 



directions. Cultivate the rare art of sa3'ino-, in the fewest 
words, exactly what you mean. 

Nearly all teachers talk too much, nearly all definitions are 
wordy, nearly everybody is guilty of the fault of verbosity. 
Some one says of a certain author: "He could suspend a 
thought no larger than the body of a fly between the wings of 
an eagle." There is something soporific in the monotonous 
sound of a teacher's voice. Compel your pupils to find for 
themselves, and for one another, words for the expression of 
their thought. 

73. Classes of !N"oiins. — The same diversity that is 
found among authors in their definitions of the noun obtains 
in their classifications of this part of speech. For example, 
one author divides nouns into two great classes — Proper and 
Common; another makes three classes — Proper, Common, 
and Abstract. The outlines shown below will further illus- 
trate this difference: 

Proper George, Boston, Nile, Hudson Riv-er. 

Many regarded as one — Con- 
gress has passed the law. 
Many regarded separately— The 
23eople are dissatisfied. 
Abstract — wisdom, truth, hai-dness. 
Verbal or Participial — To live is to think. The 
Common -* writing is distinct. 

Siti gcnc7'is (of its own kind) — This class 
includes chose nouns that have no qualities 
in common with other things, and that can- 
not, therefore, be classified — music, geometry, 
galvanism, God. 
f Class names — horse, slate, 
j Names singular — color, space. 
Common -| Names material— gold, salt. 

Collective nouns — senate, army. 
Becoming proper — Providence, the Park. 
Strictly proper — John Milton. 
Becoming common — " a Shakespeare." 
Abstract — (from adjectives) whiteness, 

honesty. 
Abstract \ ,•<-•<.•' i. 

>~ __ . . ( infinitive — to write. 

verbal in -ing — writing. 



NOUNS 



f Collective — 



NOITXS 



Proper 



Verbals — 



§ ;3 PEDAGOGICS OF GRAMMAR. 'lo 

Many other classifications might be given, but the effect 
upon the student would be only to confuse. 

With regard to common nouns sui generis, it may be 
observed that a common noun is always the name of a class of 
things. Thus, horse is the name of a class of animals, rose 
is the name of a class of flowers, etc. In other words, 
common nouns are general terms, each applicable to a 
multitude of things having certain attributes in common. 
Now, by definition, a noun sui generis never denotes a 
class, it is never used in the plural; hence, it cannot be a 
common noun. It is the name of something unique — ■ 
something unlike anything else. One author says, "The 
names of the arts and sciences are abstract nouns, because 
they are the names of processes of thought, considered 
apart and abstracted from the J^ersons that practice them. 
Thus, ninsie, painting, grammar, ehemistry, astronomy, 
are abstract noims. " It is difficult to see how abstract 
nouns can be abstracted from persons. The same author 
says, "Abstract nouns are {ii) derived from adjectives, as 
hardness, dullness, sloth, from hard, dull, and sloi^'; or (b) 
from verbs, as growth, thought, from grozu and think.'' 
That is to say, abstract nouns are derived from leords, not 
from things. 

If the aim of the author just quoted was to get rid of the 
noun sni generis,. h.e has not succeeded; for, when we take 
such nouns as galvanism, magnetism, infinity, eternity, it is 
obvious that they are not abstract noims. Neither are the}' 
common nouns, for thc}^ do not belong to classes. It is 
doubtful whether the word thing includes what is denoted 
by infinity, eternity, God, etc. If it were not that these 
terms transcend the power of the human intellect to con- 
ceive their meaning, they might be classed as proper 
nouns. 

The subject is environed with difficulty, but, in teaching 
it, such refinements are not for the pupil. They have a 
value for the teacher, however, in that they sharpen his 
powers of discrimination and classification. From the nature 
of the case, an exhaustive classification of the noun is not 



76 PEDAGOGICS OF GRAMMAR. § 3 

possible, and, for ordinary purposes, a division into proper 
and common is sufficient. Later, the common noun may be 
distinguished as collective, abstract, and verbal. Nouns siii 
generis may be called common or abstract, as the teacher 
prefers. 

It has been said that the part of speech to which a word 
belongs must be determined by its use or function in the 
sentence where it occurs. Hence, any word, sign, or char- 
acter may be used as a noun. Some examples will iHustrate 
this : 

A is always called a vowel and b a consonant. 

-f is the sign of addition and — the sign of subtraction. 

Cross your /'s and dot your e's. 

Alas is commonly an interjection. 

He answered the question without one if or but. 

[(6 X 7) + (4 X 3)] was written upon the blackboard. 

He made 7's that looked like O's. 

From these examples it will be seen that before a pupil 
can classify words, he must ascertain what office they fill in 
each particular case. 

73. Inflection of Nouns. — The word inflection is derived 
from the Latin word inficxis, a bending. It carries with it 
the idea of a change of for7n in the inflected word, and is, 
therefore, not a very fortunate term as applied to the noun; 
for the only changes of form undergone by this part of 
speech are those that denote the possessive case and those 
that indicate number. For the same reason the word declen- 
sion, which denotes the inflection of nouns, pronouns, and 
adjectives, is no better. The English language has so few 
inflections that these words, which are indispensable to the 
grammar of Latin, Greek, and many other languages, are 
to us more embarrassing than helpful. Relations that in 
other languages are indicated by endings, prefixes, and root 
changes, with us are largely determined by use or function. 
The word modification, if it were not already applied to 
mean the effect that one word, phrase, or clause has upon 
the extension or comprehension of another, would serve as a 



§ 3 PEDAGOGICS OF GRAMMAR. 77 

substitute for i/ijlcction. Indeed, many authors so use it, 
and speak oi the niodificatioiis of nouns, meaning their 
changes of form, use, or relation. 

74. Person. — The word person is borrowed from the 
stage. In Roman plays the actor wore a mask, through an 
opening in which he spoke. The word is from per, through, 
and sonns, sounding. In the uttering of a play, a discourse, 
or a sentence, there is a speaker or reader, one or more listen- 
ers, and some person or thing referred to, present or absent. 
Most closely related to the uttered matter is the speaker or 
the reader, next, the audience, and least closely related are 
the persons or things discoursed about. The nouns that 
denote these three are, respectively, in the first person, the 
second person, and the third person. 

Fii'st Person. — "I,,AV///, saw these things." 
Second Person. — '' Come, my boy, let us go." 
Phird Person. — ''Henry VIII was king of England. " 
A misconception common among pupils is that by person 
in grammar is meant a human being — a person — or the name 
of a human being. The teacher should be careful to have 
it clearly imderstood that, 

1. The name of the person or thing that is represented as 
speaking, or a substitute for a name denoting the speaker, 
is in i\\Q Jirst person. 

2. The name, or a substitute for the name, of tlie person 
or thing represented as the hearer is in the second person. 

o. The name, or a substitute for the name, of that which 
is spoken of is in the third person. 

Of course, the speaker may speak of the listener or of him- 
self in the third person. 

" The boy that has finished his work may stand." 

" The 7naH that you have honored has now the pleasure of 
addressing his constituents." 

The first .sentence refers to the "boy" as if he were absent, 
while in fact he is present as a listener. In the second sen- 
tence, "man" in the third person denotes the speaker, and 
"constituents," in the same person, denotes the audience. 



78 PEDAGOGICS OF GRAMMAR. § 3 

The speaker's reference to himself in the third person 
gives to what he says an air of modesty; and, without viola- 
ting- good taste, he may be inore complimentary to his audi- 
ence in the third than in the second person. In all such 
cases, the person of a noun or a pronoun is determined by 
its grammatical iisi% and not by what it denotes. Thus, in 
the sentences above, boy, man, and constituents are all in the 
third person. 

75. Number. — A noun is said to be in the singular 
number when it denotes only one person or thing, and it is 
in the ////rrt'/ number when it denotes more than one person 
or thing. 

The plurals of nouns are 7-egularly formed by adding i- or 
cs to the singular; but there are so many exceptional and 
doubtful cases that, with reference to very many words, the 
authorities are by no means agreed. The subject is one to 
be mastered, if, indeed, it can be mastered, by reference to 
our latest dictionaries and spelling books. Spelling, inclu- 
ding the formation of plurals, is best learned by long and 
constant practice. The teacher should prepare a list of rules 
and words belonging under each rule, and with each rule the 
exceptions to it, all abundantly illustrated by words in com- 
mon use. In addition to these, he should have a miscella- 
neous collection, and require the pupil not only to spell each 
correctly, but also, when his degree of advancement warrants 
it, to give the rule applicable. Inasmuch as the Pedagogics 
of Orthography forms one of our sections, the student is 
referred to that for further suggestions concerning the for- 
mation of plurals. 

76. Genders. — The subject of genders is a perplexing 
matter, and one upon which our grammarians are very much 
at variance. Richard Grant White argues with much heat 
that English nouns have no such distinction as gender; that 
we merely use different zvords to denote males and females. 
Thus, by king we mean a male and by queen a female exer- 
cising certain functions. In the Anglo-Saxon, the Latin, 



§ 3 PEDAGOGICS OF GRAMMAR. 79 

the Greek, and many other languages, gender is determined 
by endings, without reference to the actual sex of that which 
the word denotes. Only two gender terminations have 
descended to us from the Anglo-Saxon. These are en and 
stcr in vixen, a female fox, and spinster. In changing Lathi 
and Greek words into English words we have left behind all 
signs of their gender in the original. 

Professor Whitney, perhaps the most eminent authority in 
questions of this kind, says, "The distinctions of gender 
have been extirpated even in our nouns. To us the name 
or appellation of a person is masculine or feminine only 
according as the person is male or female; and of sex in the 
lower animals we make very small accoimt; while our Anglo- 
Saxon ancestors were as much under the dominion of that 
old, artificial grammatical distinction of all objects of thought 
as masculine, feminine, and neuter, on a basis only in small 
part coinciding with actual sex, as are the Germans now, or 
as were the Greeks and Latins of old; it was one of the orig- 
inal and characteristic features of that language from which 
all these, and most of the other tongues of Europe, are 
descended. The French has suffered the same loss only 
partially, having saved the distinction of masculine from 
feminine, but confounded neuter and masculine together by 
the obliteraticm of their respective marks of difference." 

Again he says, "Once more, man in its distinctive sense 
indicates a male animal, and we have a different word, 
wcvnan, for a female of the same kind ; and so all through 
the list of animals in which sex is a conspicuous or an impor- 
tant distinction; as, brother and sister, bull and ecn^\ ram 
and eive ; nor is there a language in the world which does 
not do the same. Only, as we have alreadv seen, our own 
family of languages (along with two or three others) has 
erected the distinction of sex into a universal one, like num- 
ber, making it a test to be applied in the use of every word ; 
breaking away from the actual limits of sex, and sexuali- 
zing, as it were, all objects of thought, on grounds which no 
mortal has yet been wise enough to discover and point out 
in detail." 



80 PEDAGOGICS OF GRAMMAR. § 3 

Some of onr authors, on the gTound that where there is no 
sex there can be no gender, give us two genders, the mas- 
culinc and the fcmijiinc; others follow the German, Latin, 
and Greek in having the masculine^ the feminine^ and the 
neuter. As to the neuter gender, they argue that the 
absence of a quality is just as distinctive a feature as its 
presence — that we make our words and our classifications as 
well from the negative as from the positive and afBrmative 
standpoints. 

A third classification of genders is into four — Diaseiiline, 
feminine, neuter, and eonunoji. This last is supposed to find 
justification from the fact that the Greek has a class of words 
called epieenes neariy equivalent to our common gender. 
But there is one important difference. The Greek common 
noun, like the German, is always preceded by an article to 
show the gender; so that while the sex of that which is 
denoted by the noun is indeterminate, the gender of the 
noun itself is known. Thus, the Greek word for fox is pre- 
ceded by the feminine article, although we cannot know the 
sex of the animal denoted by the word ; and the Greek word 
for lynx is used sometimes as masculine and sometimes as 
feminine. 

77. Etymological Parsing. — These unimportant dis- 
tinctions of gender were introduced into our earliest English 
grammars from their Greek and Latin models, and they have 
been retained, perhaps on account of the figure they make in 
etymological parsing. The more voluminous and minute 
account a pupil can give of the properties of a word, the 
more learned and important it seems to the unreflecting. 
If, however, the distinction of gender is of any real impor- 
tance, it certainly does not extend farther than to the mas- 
culine and the feiniiiine. It is important to know that cer- 
tain words are masculine and feminine correlatives; as, earl 
and countess, beau and belle, zviteh and zvisard, lord and lady, 
foal And. filly ; but what practical or disciplinary value^ can 
come from requiring the pupil to say fha-t fish, sheep, cattle, 
bird, parent^ advisor are of the comvion gender, and then to 



§ 3 PEDAGOGICvS OF GRAMMAR. 81 

add as a reason that what they denote may be either male or 
female ? 

The minute etymological parsing of the successive words 
of a sentence is an indefensible waste of time, and it is done, 
even at this late da}-, in many of our schools. The etymol- 
ogy of the words of a sentence can, in most cases, be dis- 
posed of in a very few words. The educational value that 
comes from the examination of a sentence grammatically, 
lies in its syntax and its rhetoric; these furnish discipline 
for the most important faculties of the mind. 

78. Sex and Gender. — The teacher should carefully 
distinguish between srx and gender. The former applies 
only to living beings, the latter is a property of ivords. 
Thus, the word man is of the maseuline gender, but the 
reality denoted by the word is of the male sex. 

Gender, as has been said, is a very unimportant property 
of words. Only the masenline and the feminine have any 
educational value, and these but rarely. The nenter and the 
common gender may be omitted from any attention in our 
grammar work. 

79. Cases. — Grammarians are pretty well agreed that 
case is not an inflection of nouns and pronouns, but a modifi- 
cation in their relation to other words in a sentence. A few 
definitions follow to show that relation and not inflection is 
the doininant basis of classification: 

1. " Cases, in grammar, are modifications that distinguish 
the relations of nouns or pronouns to other words. " 

2. " Case is that modification of a noun or pronoun which 
denotes its oflice in the sentence. " 

3. " Case is the _/<?;'/// given to a noun to show its relation 
to other words in the sentence." 

4. . " Case is that form or iise of a noun or pronoun which 
denotes its oflice in the sentence, or distinguishes its relation 
to some other word in the sentence." 

5. " Case is the relation of a noim to some other word in 
the sentence. " 



82 PEDAGOGICS OF GRAMMAR. § 3 

It will be observed that all but the last of the foregoing 
definitions agree in making the case of nouns and pronouns 
dependent upon their form or their use. Definitions 1 and 2 
make case a modification^ 3 makes it Sifortn, 4 Siforin or use, 
and 5 makes it the relation itself. Now the exact facts are 
that with noiuis the possessive case is determined, in both the 
singular and the plural, by form or inflection^ and the other 
cases by use or function. With pronouns, case is almost 
wholly denoted by different words. Thus, without seeing 
/, 2iu\ thou^ he, she, and they in sentences, we know that, 
when they are correctly used they must be in the relation of 
the nominative case ; and we know also that me, us, him, and 
them must be tised in the objective case. The noun, except 
it be in the possessive case, must be used in a sentence before 
we can determine its case; hence, the case of the noun is 
known from its use or office. 

The pronoun you, in the nominative and objective, both 
singular and plural, and the same cases of //, in the singular, 
are determined by use or function; for, in these cases, their 
forms are alike. 

The relative and the interrogative pronouns have different 
words for the several cases. 

It may be added that case is not a relation, as is said in 
definition 5, but the form or use of a word denotes its relation 
with respect to case. The second part of definition 4 is 
intended to provide for the possessive case; but this addition 
is not necessary, since \h.Q form of the word denotes the rela- 
tion of possession, origin, etc. 

Perhaps the student will accept the following definition as 
more in consonance with the facts, and as avoiding the use of 
the term nwdifieations, which in this work has been set apart 
for another use : 

Case is the form or the use of a noun or a pronoun by 
wJiich is denoted its relation to other words in a sentence. 



PEDAGOGICS OF GRAMMAR. 

(PART 2.) 



1. What Is Meant by Relation. — One of the most 
difficult terms of grammar for pupils to understand is that of 
relation; and, if it be at all possible, the teacher should make 
its meaning plain. So long as the relation between two 
things is merely physical, the notion is easy to grasp. Thus, 
the relations of father and son, of mother and daughter, 
of brother and sister are all very obvious. The relation 
of position is less easy to be comprehended, yet it can, with 
little difficulty, be perceived by pupils of average intelligence. 
An object may be on, under , or above the earth; a pupil may 
be ///, near, bj\ aioay from school. The business of a 
detective is to establish relations between persons, acts, 
times, places, etc. Thus, some goods are stolen; a detect- 
ive discovers similar goods in the possession of a suspected 
person. His first thought is to establish the relation of 
identity or sameness between the goods he has found and 
those stolen. This having been done, his investigations 
are continued in the effort to combine relations of time, 
place, and other circumstances, so as to convert the relation 
oi probability into that of certainty. 

Cases where relations are not physical, but metaphysical 
and logical — merely conceived — present greater difficulty. 

§ 4 



2 



PEDAGOGICS OF GRAMMAR. 



Such are those in grammar. The relations between subject 
and predicate, subject and object, the modifier and the word 
modified — ^hese are seen but vaguely by pupils. The prep- 
osition furnishes the teacher an excellent means of showing 
how words entirely unrelated may be brought into relation. 
Thus, the words live and river are without connection, 
except that of nearness on this page, but other relations 
may be established between them. 



i, J J- .1 
Live ■{ 



over 

by 
near 

in 

up 
down 

on 

etc. J 



the river 



Walk \ 



around 

in 

through 

across 

to 
from 
over 
etc. 



the city. 



At least two concepts are necessary before relation can be 
said to exist. Thus, the words length, lueight, fraternity^ 
proximity, hope, fear, etc. express relations each involv- 
ing two or more things. In asserting that something is 
of a certain length or weight, some measuring imit is 
implied; when the relation of fraternity exists we under- 
stand that there are tAvo or more brothers; etc. The clear 
statement of such relations is important, but somewhat 
difficult. 

The teacher will notice that relations are expressed by 
abstract nouns, and it will probably occur to him that to 
give a list of such nouns to a class, and require the pupils to 
mention two things realizing the expressed relation, is a good 
exercise. 



3. ISTuniber of Cases. — The word ease is derived from 
the Latin casus, a falling. This term and the words decline 
and declension, a leaning from, or down, are derived from 
the Latin notion that the nominative is the tiprigJit case 
[casus rectus), the uuin/lccted case, and that the others lean 
axvay from it — are inflected, or declined. 

From this arises the fact that our orammarians have 



PEDAGOGICS OF GRAMMAR. 



invested our language with a varying number of cases. 
Professor Meiklejohn says, "We mnv employ five cases: 
nominative, possessive, dative, objective, and voca- 
tive/'' This bringing into English grammar distinctions 
belonging in some other language arises partly from our 
human instinct for discovering likenesses and resemblances 
even when they have no existence, and partly from an 
almost irresistible impulse to generalize and classify. But 
there is no more reason for saying that we use the dative 
case in, "I gave [to] hiJii a dollar," "I bought [for] him a 
sled," than there is for calling 
hij/t ablative in, "I went with 
[from, by] hijii.'" In Latin the 
dative is translated to or for some 
person or thing, and the ablative 
7oith, from, in, or by the person 
or thing. If we must have the 
dative case, let us, by all means, 
have the ablative. Most gram- 
mars call the dative the case of 
the indirect objeet, and the ablative they call the objective 
after a preposition. This is clearly better and simpk-r 
than to import terms that have scarcely been Anglicized. 

The vocative is really the nominative — it merely names. 
To distinguish the various forms of the nominative case, we 
have the nominative case by address, by pleonasm, and the 
nominative case absolute or independent, besides the ordinary 
use of the nominative as the subject of a finite verb. We 
really need, in our grammars, only three cases: nouii)iative.. 
possessive, and objective. The numerous relations expressed 
by the preposition and its accompanying object do not 
require to be divided into a great variety of cases. There 
can be no defensible reason for calling the to and the 
for relation, dative, and ignoring the at, against, accord- 
ing to, and other relations. If, as some say, oi;r language 
is indeed a " grammarless tongue," any attempt to make 
a grammar for it should at least be characterized by sim- 
plicity. 




PEDAGOGICS OF GRAMMAR. 



TABI.E OF THE :N^0UI^. 

C First person ] 

r 1 Tt o J Denoted bv function or 

f 1. Person 4 Second person - ■' 

relation. 

(^ Third person J 

f vSingular 1 
2. Number i ]• Denot^^d by intiection. 

1 Plural J 



^ r Masculine ) [ ''^"^^^es; as, actor, actress. 

gi I I Denoted I P^-efi-^es; as, he-goat, she- 



^ 



3. Gender ■{ Feminine ;^ -; goat. 

bv 



[ [Neuter] J 

I' Nominative — Denoted by function. 
4. Case - Possessive — Denoted by inflection. 

I Objective — Denoted by function. 



Different words ; as, man, 
woman. 



THE PROXOUX. 

3. Deflnition of a I'l'onoiiu. — The word pronoun is 
derived from pro, for, and nouicn, a name. Its derivation, 
therefore, would seem to indicate that its definition should 
be, "A pronoun is a word used instead of a noun," and this 
is the usual definition. Its function in the sentence is not, 
however, always to take the place of a noun. In the sen- 
tence, "John sold John's dog, and for the dog- John received 
five dollars," we may substitute pronouns for the nouns after 
their first occurrence. Thus, "John sold Jiis dog-, and for 
// lie received five dollars." Here, there is no question that 
the pronouns are merely substitutes for the nouns. But 
with pronouns of the first and .second persons, no such sub- 
stitution is possible; for if it were, then we should be able, 
without change of sense, to put nouns in place of the pro- 
nouns in the following sentence: "I shall send you (mean- 
ing my dog) back to your former master, for you are of no use 
to me." The pronouns /, wc, 2ay^ you serve only to indie te 
that some person is speaking, or that some one is spokc-n 'o. 
The speaker and the hearer are assumed as known, or their 
personality may be a matter of indifference. Thus, a man 



§ 4 PEDAGOGICS OF GRAMMAR. 5 

with something- to sell may gather a crowd on the street. 
He refers to himself as /, to his audience a.s jo7i, w/io, cohoin, 
and to his wares as //, thty, this, thejn, these, lohieh, etc. 
Indeed, the anteceelent, or the noun that is represented by a 
pronoun, is implied or taken for granted as often as it is 
expressed. 

On grounds such as these the ordinary definition: 

A pronoiiu is a i^'ord used instead of a noun, has been 
very generally criticized. The writer, therefore, ventures to 
propose the following substitute: 

A pronoun is a luord used to denote persons or things 
without naming them. 

By this all the objections mentioned above are avoided, 
and it serves to meet every requirement of a correct scien- 
tific definition. 

4. Classes of Pronouns. — The classification of pronouns 
is different with different authors; some give three, some 
four, and others five, classes. Goold Brown has Personal, 
Relative, and Interrogative; many others make four classes, 
Personal, Relative, Interrogative, and Adjective; and a late 
and eminent authority divides them into Personal, Relative, 
Interrogative, Demonstrative, and Indefinite. Examples of 
these classes are given below: 

1. Personal ; usually denoting persons — /, zve, vu\ us, 
thou, thee, you, he, her, she, him, they, them. 

2. Relative ; relating or pointing to a word or other 
expression called the antecedent — ^cho, luhieJi, what, that, 
and sometimes as and but. 

3. Interroj»-ative ; used in questioning — who / whieJi ? 
zvJiat / 

4. Demonstrative ; distinctly indicating some person or 
thing {lienionstrare, to point out, as with the finger) — this, 
that, these, those, former, latter, same, sueh. 

5. Indefinite; vaguely and indistinctly denoting per- 
sons or things — any, some, other, another, eaeJi, every, either, 
neitJier, etc. 

For use in the classroom, the foregoing is perhaps the 



6 PEDAGOGICS OF GRAMMAR. § 4 

best classification that has so far been made. In order to 
avoid confusion, the many bewildering subdivisions that 
have been devised by various authors are omitted. There 
is, however, a distinction in the use of many of the pronouns 
that is of importance, and to it we owe the class called : 

5. Adjective Pronotiiis. — A pronoun that modifies a 
noun becomes, for that reason, an adjective pronoun, or a 
pronominal adjective. But when a pronoun is used in its 
simple representative function — when it merely denotes per- 
sons or things — it belongs in one of the five classes given in 
the preceding paragraph. The following sentences will 
make clear the distinction between words used as adjective 
pronouns and the same words used as pronouns : 

My hat was torn during that rough play. 

Uliat game did you kill yesterday ? 

These men are my friends, but I am not to mention their 

names. 
Can such things be ? 
Some fault may be found, but another person might have 

committed the same offense. 
I like these, but I prefer those. 
One sows, another reaps. 
This is good, but that is better. 
Either will do, though neither is quite what I want. 



Adjective 
Pronouns. 



Pronouns. 



■ Certain forms of the personal pronoims, when used inde- 
pendently of a noun, are called: 

(>. Absolute Possessive Pronouns.— These fonns are 
mine, t/iine, onrs, yonrs, his, hers, theirs. They are ec^uiv- 
alent to a noun used with an adjective pronoun modifier. 

^^ Mine and j'onrs together are worth more than his and 
hers." If the reference here is to books, for example, the 
sentence is exactly equivalent to " My books and yonr books 
together are worth more than Jus books and Jicr books. " 

These pronouns, although they denote possession, are never 
used in the possessive case, and they occur in both numbers; 

" Mi)ic was lost and I took his.'' 

" His were large, but niine were very small." 



§ 4 PEDAGOGICS OF GRAMMAR. 7 

Mine and thi)ic are used also as adjective pronouns before 
nouns beginning with a vowel, especially in poetry, 

'•'■Mine eyes have seen the glory of the coming of the Lord." 
" TJiine ears are open to the cries of the oppressed." 

7. Ambiguity From tlie Use of Pronouns. — There is 
no part of speech requiring more care in its use than the 
pronoun. If the student will carefully examine the writings 
of our best authors, he will notice a studied avoidance of this 
class of words. When a sentence contains but one possible 
antecedent of a pronoun, no ambiguity is likely to occur; as, 
" The boy lost /!/jr hat. " But when there are two or more 
words, any one of which inay be the antecedent, it is certain 
that the sentence will be ambiguous; as, "William assured 
John that Jtc should be much pleased if lie could attend his 
party." The following sentence, quoted by Cobbett from 
The Rambler^ is notable for want of clearness: 

" Melissa brought with her an old maid recommended by her 
mother, luho taught her all tlie arts of domestic management, and 
was, on every occasion, her chief agent and directress. They soon 
mvented one reason or [an] other to quarrel with all my servants, and 
either prevailed on me to turn tlion away, or treated //win so ill that 
//wy left me of //u';/ist'/7'rs, and a/-a'ays siipp/icd //leir p/accs with 
some brought from my wife's family." 

Was it the mother of Melissa that recommended the old 
maid, or did the old maid's mother do it ? Who was the 
teacher and who the pupil in " the arts etc."; who was the 
" chief agent," and whose chief agent was she? The ante- 
cedents of the pronouns in the next sentence are almost as 
indefinite as those in the fir.st sentence, but the matter need 
not be pursued further. The teacher will see the propriety 
of the following suggestions: 

1. Use the pronoun only when you ean do so without 
ambiguity. 

2. See that your pupils are well trained in finding and in 
correcting errors in the use of pronouns. 

8. Compound Pronouns. — Of the five classes of pro- 
nouns enumerated above, the personal and the relative 



8 PEDAGOGICS OF GRAMMAR. § 4 

assume compound forms. The simple personals become 
compound by the addition of self iov the singular and selves 
for the plural. Thus, myself, ourselves, thyself, yourself 
yourselves, hijnself herself, itself, themselves. In the first 
and second persons only the possessive forms, my, our, thy, 
andjw/r are compounded with self while in the third per- 
son only the objeetives Jiim, her, it, and tJieui are used in 
these compounds. 

The simple relatives, in all their case forms, are com- 
poiuided by adding ever or soever. Thus, whoever, whoso- 
ever ; whosesoever ; zvhomever, wJiomsoever ; whichever, 
whiehsoever ; ivhatever, whatsoever. 

There is a colloquial use of certain compound forms of the 
interrogative pronouns ; these, of course, should be avoided. 

Whoever can it be ? Whatever does he want ? 

Whoso is frequently used in the Bible, and in some of our 
poets, notably Whittier, In Carhde we find, " . 
which whoso wished might come and examine." Whatso is 
also used by early writers. 

9. The Relative ''What.'"' — The pronoun ^vhat is by 
many grammarians said to be a double relative, equivalent 
to that whieh or the thing which ; and to illustrate, they give 
such sentences as "Tell me what you want." "Explain 
what caused the trouble." In such constructions, they 
separate zohat into that %vhich or the thing ivhicli, and say 
that, in the first sentence, that is the object of tell and 7uhich 
the object of %vant. The second sentence, they expand into 
" Explain the thing that (or tJiat wliieJi) caused the trouble." 
Then, thing or that is said to be the object of explain, and 
that or luhich the subject of caused. To this it may be 
objected that these writers do not account for what, but for 
its supposed equivalent, that which or the thing zchich. This 
use of zi'hat is good idiomatic English, and its double func- 
tion of object of two different clauses, or of object of one 
clause and subject of another, with an added connective 
function in both cases, no more requires its reduction to 
other terms than does the case of any other word performing 



§ 4 PEDAGOGICS OF GRAMMAR. 9 

two offices. Thus, in the sentence, '' His work is neater 
than hers," it is not considered necessary to explain the 
grammatical function of hers by accounting for its equiva- 
lent, her work. Besides, consistency would suggest the same 
kind of reduction of luho and whom in the following sen- 
tences: "Tell me who you are." "Mention zvJioin you 
seek." Such treatment of these sentences would result in, 
"Tell me the person who you are." ''■Isilention the person 
ivhoni you seek." In all these cases the unexpressed ante- 
cedent is revealed by reducing the relatives to other terms, 
but by so doing we are not disposing of the sentences as they 
were, but of others that are assumed as equivalent to the 
original. The relative whieh can be treated in similar 
fashion. 

The writer would suggest that tvhat be called a iioublc 
rehitive, and that its functions with respect to both clauses 
be pointed out and its connective office mentioned. This is 
exactly similar to our treatment of tlie eonjunetive aifverb, 
the adjective pronoun, and the absolute possessive personal 
pronoun. 

"He died where he lay." "You have torn my coat." 
^^ Mine surpass j'cj;//'.s- in quality." 

It would manifestly be absurd to change " He died where 
he lay" to "He died i)i the place in zuhich he lay." We 
prefer to say that cohere modifies the meaning of both ve:bs 
and connects the two clauses. It is not amiss to empha.size 
here what was said before : Do not needlessly dismendnr a 
good English sentence, or supply imaginary ellipses. 

Of course, there are many ellipses about which there can 
be no question. Thus, "Henry ate his supper, and [he] 
studied his lesson." "The boy went away, and his sister 
also [went awayj." By "imaginary ellipses " we mean such 
as, "The sled is zvorth a dollar" = "The sled is worthy of a. 
dollar" = "The .sled is of the worth ofn dollar." Or, " The 
interjection," some authors say, "is an entire sentence con- 
densed into one word." Thus, "vShame!"= "You should 
be ashamed of yourself." Of course, no one can, with any 
certainty, expand an interjection into a sentence. 



10 PEDAGOGICS OF GRAMMAR. S 4 



TA35I^1^ OF THE PROXOI I^. 

i Simple. 
1. Personal J, 

{ Compound. 

.„, ,2. Relative 3 f^^^P^^" ^ 

I Classes -; | Compound. 

3. Interrogative. 

I 4. Demonstrative. 

[ 5. Indefinite. 

r Gender. [Only certain personal pro- 

! Person. nouns intlie singular have 

j Number. gender.] 
[Case. 



Properties 



THE ADJECTIVE. 

10. Derivation and Office. — The word adjective is 
from the Latin adjectivus, added to. The term implies that 
the adjective is always joined directly to the noun or pro- 
noun modified by it, but such is not the case. " Good, sweet, 
and beautiful though this little g'irl was, etc." " This little 
girl was g'ood, sweet, and beautiful." 

The term viodifieation has already been explained as any 
means of determining the modus or measure in which the 
meaning of a word, phrase, clause, or proposition is to be 
taken. The primary and distinctive function of the adjective 
is to do this with nouns and pronouns. The teacher will, of 
course, note that words are not modified, but their i/ieauiiigs ; 
so that an adjective is not, as many say, a word used to 
modify a noun or a pronoun, but it is a word used to modify 
the iiieanvig of a noun or a pronoun. It should be noted, 
however, that for the sake of brevity it is allowable to say 
that adjectives modify Jiouiis and pronouns, that adverbs 
modify verbs, etc. 

The teacher should have a distinct notion of what is meant 
by the extension, and what by the eomprehension of a term. 
If a word, say a noun, has no other word joined to it to 
modify its meaning, its extension is nnliniited, universal, 
general, and its comprehension is the narrowest possible — 



§ i PEDAGOGICS OF GRAMMAR. 11 

mere existence. Thus, apple includes every object in the class 
that the word denotes. But when the term red is joined to 
apple, the extension is narrowed, — not so many apples are 
included, — but the comprehension of the terra is enlarged. 
We know more exactly what kind of apple is meant. To the 
notion of mere existence is added that of color. Large red 
apple comprehends existence, color, and relative size. That 
is, the extension of a term has reference to the number of 
objects to which the term may be applied — to the extent of 
its applicability; the eoviprehension of a term or a collection 
of terms has reference to qualities expressed — not implied, 
denoted — not eonnoted. The teacher should here recall the 
law of the inverse ratio between the extension and the com- 
prehension of terms. This law may be thus expressed: 
Each modi fier that is added to a term increases the definitoiess 
of the mental picture, and diminishes the range of objects to 
ivJiich the modified term is applicable, and the reverse. It will 
be obvious, therefore, that adjectives of every class modify 
the meaning of nouns and pronouns; that is, they limit or 
narrow their extension and enlarge their comprehension. 

11. Definitions of tlie Adjective. — Remembering 
these general observations, let us examine some of the 
definitions of the adjective that are found in otir textbooks: 

1. "An adjective is a word joined to a noun or a pro- 
noun to limit or qualify its meaning." 

2. " An adjective is a word used to modify a noun or a 
pronoun." 

3. " An adjective is a word used to modify a noun or a 
pronoun without representing an object." 

■1. " An adjective is a word used to qualify or //;//// the 
meaning of a noun or a pronoun. " 

5. "An adjective is a word added to a ncnin or a pro- 
noun, and generally expresses quality." 

6. " An adjective is a word used to limit or qtuilify the 
application of a noun or a nominal phrase." 

The student should be able to find much interest and 
profit in comparing and criticizing these definitions. They 



12 PEDAGOGICS OF GRAMMAR. § 4 

are all taken from well known authorities, and the surprising 
thing about them is that they differ so widely. In such exam- 
ination, the first question likely to occur is as to the precise 
differences in meaning of hmt^, qualify^ and modify. These 
terms have been considered at some length in Art. 28, 
Pedagogics of Grammar, Part 1, which the student is 
advised to read again with care. 

As used by most grammarians, it seems to be intended 
that /////// shall have reference to adjectives denoting num- 
ber, size, or mass. Such are three, third, some, many, any, 
every, large, small, vast, immense. This, however, cannot 
be asserted positively. The truth is that even very careful 
writers often employ words without considering how niuch 
is included in, and how much excluded from, their meaning. 
But strictly, all adjectives /////// — determine the extension of 
the meaning of nouns and pronotms — and all adjectives also 
modify. We may, therefore, use the two terms interchange- 
ably, preferring, however, the word modify on account of the 
fact that all writers agree in using it in its wide generic sense. 

Definition 1 is objectionable for three reasons: first, 
because the adjective is only sometimes "joined to a noun " ; 
secondly, because of the vagueness of "limit or qualify"; 
and thirdly, because an adjective modifies, not a noun or a 
pronoun, but the meaning of a noun or a pronoun. Defini- 
tion 5 is open to the first of these objections, and is, besides, 
unfortunate in its last clause. Definitions 1, 4, and 6 contain 
" limit or qualify," and the last would be better without " or 
a nominal phrase," by which is meant a substantive or noun 
phrase. In definition 3, "without representing an object" 
is intended to exclude from among adjectives the absolute 
possessive pronouns mine, thine, etc. ; but, unfortunately, it 
excludes, as well, adjectives denoting material; as steam- 
hamiuer, r^(7/-shovel, etc. 

Providing against these objections is not a difficult matter. 

An adjective is a word used to modify the meaning of a 
noun or a pronoun. 

This definition is brief, and it provides for both the exten- 
sion and the comprehension of the noun's meaning. 



g 4 PEDAGOGICS OF GRAMMAR. 13 

12, Classification of Adjectives. — Equally various are 
the divisions that different authors have made of adjectives. 
Many authorities give two classes of adjectives — qualifying 
and limiting. The diiliculty in this classification lies in the 
uncertainty of the word qualifying. The logicians and meta- 
physicians have not yet been able to agree as to the meaning 
of the term quality; and it is upon this that the meaning of 
qualifying depends. One authority says, "Quality is an 
element of anything, and aids in making it distinct from 
other things; the attributes or characteristics of anything as 
determining its place, rank, value, etc." 

This definition seems to cover every function of the adjective, 
for certainly every adjective aids the mind in making one thing 
or group of things distinct from other things. The adjective 
does this by denoting some characteristic of place, rank, value, 
number, quantity, etc., or of properties that address the mind 
through the senses. In short, every adjective denotes some 
quality belonging to the thing named by a noun. But the divi- 
sion of adjectives into two classes, qualifyinga.nd limit ing.^ or 
into three, qualifying., limiting., and numeral., is very common. 

13. Brown^s Classification. — Remembering, however, 
the vagueness of the term qualifying., and that all the adjec- 
tives limit — fix boundaries — let us consider one of the best 
known classifications — that of Goold Brown. His divisions 
and definitions are as follows.: common, proper, numeral, pro- 
nominal, participial, and compound. 

I. A common adjective is any ordinary epithet, or 
adjective denoting quality or situation; as, good, peaceful, 
eastern, outer. 

II. A propel* adjective is an adjective formed from a 
proper noun ; as, A merican, English, Mil tonic. 

III. A nnmeral adjective is an adjective that expresses 
a definite number; as, one, tzvo, three, four, etc. 

IV. A pronominal adjective is a definitive word which 
may either accompany its noun, or represent it understood; 
as, "^//join to guard what each desires to gain." ^^ All 
men join to guard what each man desires to gain." 



14 PEDAGOGICS OF GRAMMAR. § 4 

V. A participial adjective is one that has the form of 
a participle, but differs from it by rejecting the idea of time ; 
as, an aumsing story. 

VI. A compound adjective is one that consists of two 
or more words joined either by a hyphen or directly; as, 
nnt-broivn, laughter-loving, four-footed, lovesick. 

14. Criticism of Bro^vn's Classes. — Of these classes, 
it may be remarked that : 

1. Most, if not all, compound adjectives are "epithets," 
though some of them may not be '^ordinary epithets." 
Hence, VI might better be included under I and II. The 
Franco-Prussia)i war, a self-made man, a dozvncast look — 
these are epithets. Some compound adjectives belong 
among the numerals; as, a six- fingered hand, a five-toed 
bird, a six-pctaled flower. These also are epithets. Class 
VI, then, seems to be superfluous. 

2. If words are to be classified strictly in accordance 
with their rise, IV should read, "A pronominal adjective 
is one having the double function of adjective and pronoun " ; 
as, my hat, some men, every person. It is nndonbtedly better 
to call such words pronouns when they have no accompany- 
ing noun. U.sed to modify a noun, they are adjective pro- 
nouns or pronominal adjectives. 

15. Professor MeiklejohnN Classes.— Another classi- 
fication, which the student may prefer to Brown's, is that of 
Professor Meiklejohn. He divides adjectives into four classes, 
which he defines as follows : 

I. Qualitative adjectives denote a quality of the sub- 
ject or thing named by the noun ; such as, blue, sad, big, 
little. 

II. Quantitative adjectives denote either quantity or 
tjtdefinite number; and they can go with either the singular 
or with the plural of nouns, or with both. The following is 
a list : any, all, both, certain, divers, enough, feu>, little, 
many, much, no, several, some, whole. 

III. Numbering or numeral adjectives express the 



§ 4 PEDAGOGICS OF GRAMMAR. 15 

)iuiiihcr of the things or persons indicated by the noun. 
They are generally divided into 

1. Cardinal iiiinierals ; as, onc^ fi'<-'<'\ nine. 

2. Ordinal numerals ; as, first., fifth, ninth. 

IV. Demonstrative adjectives are those used to point 
out the thing expressed by the noun; and besides indicating 
a person or thing, they indicate a relation either to the 
speaker or to something else. 

Demonstrative adjectives are of three kinds: 

1. Articles. 2. AdjectiA'e i^ronovms. 3. Ordinal 
numerals. 

Adjective pronouns can be used either as adjectives i^'itJi 
the noun, or as pronouns for the noun. They are divided 
into the following classes: 

1. DemonstratiA'e adjective prononns ; as, this, these, 
that, those, yon, yonder. 

'I. Interrogative adjective prononns ; as, which ? 
li'Jiat / whether {of the t7c>o) .^ 

3. Distributive adjective pronouns ; as, eaeh, every, 
either, neither 

\. Possessive adjective j)ronouns ; as, my, thy, his, 
her. 

16. Articles. — It is not many years since the article was 
recognized by all grammarians as a separate part of speech. 
No one thought of classifying it among the adjectives. But 
later, grammarians came to see that a and an are as much 
adjective in their function as one, and that tlie and that 
belong in the same class. Goold Brown, in his "Grammar 
of English Grammars," argues in favor of retaining a, an, 
and tJie in a distinct class. His arguments failed, however, 
for the grammarians of today are of one opinion with refer- 
ence to this subject. The article is merely an adjective, and 
it will doubtless continiie to be so regarded. We may expect 
soon to see a and an placed in the class called by Professor 
Meiklejohn Quantitative, and tJie is already found with tJiis 
and tJiat among the Demonstratives. 



16 



PEDAGOGICS OF GRAMMAR. 



§4 



1 7 . Anotlier Classification. — In the belief that it is pos- 
sible to improve upon the classification of adjectives hitherto 
given, the foregoing is submitted, which will perhaps be found 
more exact and useful for classroom work. Brown's common, 
proper, participial, and compound adjectives all belong under 
the general class of Qiialitativcs. His numerals and some of his 
pronominals are Quant itativcs, and the rest are Demonstratives. 

Professor Meiklejohn's numerals are more exactly classed 
as Quantitatives and his ordinals belong in the same class, 
although he makes some of them numeral and some demon- 
strative. 



TABLE OF THE ADJECTIVE. 

1. Common 



M 

"W 

<! 



Quantitative 



Demonstrative \ 



Simple — good, wise, happy. 
Compound — four-handed, blue- 
eyed. 



r Qualitative \ 2. Proper 



( Simple — Russian, English. 
i Compound — Anglo-American. 



f Simple — amusing, pleasing. 
L 3. Participial i Compound— life-giving, wool- 
I gathering. 



r 1. Definite 



Indefinite 



1. Article 



Common — whole, no, enough, 
both, all. 

Cardinal — one, six. 



I 



Numeral 



Ordinal — first, sixth. 



Common — some, much, little, 
any. 
I Numeral — any, few, some, 
I several, divers. 



i D. 
I In 



Definite — the. 
definite — a, an. 



Adjective 
Pronoun 



Common — this, these ; that, 

those ; yon, yonder. 
Interrogative — which ? what ? 

whether ? 
Distributive — each, either, 

every, neither. 
Possessive — my, thy, his, her, 

their. 



§ 4 PEDAGOGICS OF GRAMMAR. 17 

18. Remarks on tlie Table. — To make 2^ pc7'fcct classi- 
fication of the adjective is perhaps impossible. This arises 
from the fact that some of the adjective pronouns, as sonic, 
few, all, many, etc., are quantitativcs as well. Instead of 
making- numeral and quantitative subdivisions of demonstra- 
tive adjective pronouns, it has been thought better to make 
them definite and indefinite quantitativcs. This table has 
been thoroughly tested in the classroom, and has been found 
to work well. Even if etymological parsing be reduced to a 
minimum, accin-ate classifications of the parts of speech are 
indispensable. They furnish a discipline in orderly and log- 
ical arrangement that can be acquired so well in no other 
exercise. The teacher can greatly benefit his pupils by 
requiring- them to criticize and rearrange the tables given in 
the textbooks. If two or more different tables of the same part 
of speech be put upon a blackboard, and copied for home 
study and reclassification, the work maybe made of absorbing" 
interest. 

IXFLECTIO:?^ OF ADJECTIVES. 

19. Comparison of AdjeetiAes. — Grammarians tell us 
that there are three degrees of comparison, positive, compar- 
ative, and superlative. There are, however, many more, as 
will be shown hereafter; but in oi:r textbooks, those just 
mentioned are the only ones explained. Grammatical 
comparison ascends and descends from the positive. Thus, 

Sitperlatii'e. Coiiiparatrec. Positive. Comparative. Superlative. 
least good, less good, Good, better, best, 

least bad, less bad. Bad, worse, worst. 

It is obvious that, on both sides of the positive between it 
and the superlative, there are, besides the regular compara- 
tive, many intermediate degrees of quality. This is due to 
the fact that the regular comparison has in it nothing of 
mathematical precision. Better Sir\6. best may be only slightly 
beyond good, or they may be very much so. The only cer- 
tainty expressed is that best denotes a higher degree of the 
quality of goodness than better, and better a higher degree 
than good. But the extent of a quality comprehended 



18 



PEDAGOGICS OF GRAMMAR. 



between the positive and the superlative may be very great 
or very little, and the comparative is not to be regarded as an 




exact mean between the positive and the superlative. These 
statements are illustrated in the accompanying diagrams. 

The primitive and fun- 
damental idea of quality 
or attribute is expressed 
by the positive form of 
an adjective. The other 
degrees were originally 
only intensive and not 
inflectioiial forms of the 
positive. Indeed, at first 
the noim and the adjective 
had, in general, the same 
form, and whether a word 
was used as a noun or as 
an adjective was revealed 
only by the context. In 
the gradual evolution of 
the language, the process 
of finding expressions for 
differences gave, in general, distinct forms and well defined 
functions to these two parts of speech. Many of them, 




§ 4 PEDAGOGICS OF GRAMMAR. 19 

however, retain their original identity of form, and this is 
true not only of words derived from the Anglo-Saxon, 
but also of those taken from the Greek and the Latin. 
Numerous illustrations will readily suggest themselves to 
the student. 

30. The Positive Degree. — Some interesting psycho- 
logical considerations are involved in the process of arriving 
at the notion of the positive degree of an adjective denoting 
quality or quantity. The botanist notices that flowers 
resemble, and differ from, one another, and that, taken col- 
lectively, they approach a certain type having more or less 
likeness to every known flower. This typical flower is, as it 
were an average in structure of all flowers; and, as is the 
fact, it has no perfect realization in nature; but in studying 
any given flower, it is necessary only to note how it resem- 
bles, and how it differs from, the typical flower. 

In a similar way, when we consider houses with respect to 
the use for which they were intended, we form a general 
notion of what constitutes usual or average size. As com- 
pared with that size, we pronounce a certain dwelling house 
large, a larger house intended as a church we call small, and 
a house still larger, if intended for a palace, is also small. 
This general type is derived from observation — from expe- 
rience. The African, whose home is a mere hut, would be 
unable to find adjectives to denote what to him would be 
the enormous size of an average home in a civilized 
country. 

So that there is an appeal to experience in every instance 
when we use the positive degree. The object in which a 
certain quality inheres is compared with the type or average 
of that quality, and by the comparison we are enabled to say 
that the object is Jiot or cold, icet or dry, long or short, large 
or small. This reference to the standard is not formal, 
minute, and deliberate, but, as we say in grammar, it is 
implied, or assumed. The comparison is so quickly and 
easily made that it is a matter of mere instinct or intuition — 
it is involuntary. Without delay, the assertion of the quality 



20 PEDAGOGICS OF GRAMMAR. § 4 

as belonging to a certain object, follows this instantaneous 
reference to the type. We say, "The day is cold," and it 
is not necessary to compare its temperature with that of 
every other day in our experience. We have long since con- 
ceived a notion of average coldness, and the comparison is 
with this notion, and not with the days that furnished it.' 

It may be observed, however, that these general notions 
are not fixed and uniform, but relative to isach individual 
experience. A cold day to an Eskimo is very different from 
a cold day to an inhabitant of a temperate or a tropical 
climate. 

We begin to form this type or general notion only when 
we have' observed vun'c than one of the objects possessing the 
qualit}'. A child, seeing for the first time an elephant, is 
not prepared to say whether it is large or small. He may, 
indeed, refer it to the larger class anivia/, to which his dog 
and cat belong, and .say, "It is a large animal " ; but he 
cannot say, " It is a large elephant." There is no long inde- 
pendent of longer and less long, or short. Hence, psycho- 
logically. 

Definition. — An adjective is in the positive degree zvhen 
its meaning earries an assumed or implied comparison zvith 
respect to some attribute common to an indefinite number of 
objects. 

21. Some Definitions Compared and Criticized. — 

The following definitions are quoted from standard authori- 
ties: 

1. " The positive degree is the simple form of the 
adjective." 

2. "The positive degree expresses simple equality." 

3. " The positive degree is that which is expressed by 
the adjective in its simple form." 

4. "The positive degree of an adjective is the adjec- 
tive without modification, used to denote simple quantity or 
quality." 

5. "The positive degree of an adjective is its simple, 
michanofed form." 



§ 4 PEDAGOGICS OF GRAMMAR. 21 

Most of these definitions make simple form or zvaiit of 
modification the basis of classification; others make expres- 
sion of simple quality the test of the positive degree. But it 
should be noted that adjectives in all degrees express simple 
quality, and that such words as better^ best, zcorse, more, 
most, less, etc. are simple forms. There is no simpler form 
of better, for certainly ^ood is not a form of it. Then there 
are certain words not capable of comparison. To apply to 
them the expression simple form would imply that they 
have other forms not simple. Such words as triangular, 
iiifnite, eubieal, linear, immeasurable, inconeeivable, gal- 
vanic, etc. belong in this class; and these words all express 
simple quality or quantity, and are generally treated as 
positives, though the notion of degree implies at least two 
objects. 

The definition given above by the writer is from the 
standpoint of the exact function of the adjective, and does 
not consider as material its form, which is a matter of imcer- 
tainty. Moreover, the definitions of the comparative and 
superlative degrees follow from it as easy inductions. 

Definition. — An adjective is in the comparative deg'i'ee 

wJien it denotes an actual comparison of t-\vo objects li'ith 
respect to some common attribute. 

Definition. — An adjective is in tJte superlative degree 
ivJien it denotes an actual comparison of a defiiiite number 
of objects, not less than tliree, with respect to some common 
attribute. 

The student should carefully discriminate between an 
assumed comparison and one that is actually made. " John 
is a tall boy " assumes a previous comparison of boys in gen- 
eral, with respect to tallness, and the establishment of an 
average or type. It is only after comparison with this type 
that we are prepared to assert his tallness. 

" John is taller than James " denotes an c?r///c?'/ comparison 
of the two. 

"John is the tallest boy in the party " denotes an actual 
comparison among a definite number — the party. 



22 PEDAGOGICS OF GRAMMAR. § 4 

3^. Other Expressions of Comparison.^ — In his 

" Life and Growth of Language," Professor Whitney says: 
"For a part of our adjectives of quality, we have forms 
denoting two "degrees" of increment: Jiigh, highc?-, high- 
est ; . . . . But, as means of comparison, they cover only a 
small part of the conceivable ground, and cover it only 
rudely. The possible degrees of a quality are indefinitely 
numerous, and there are descending as well as ascending 
grades, which have in theory an equal right to notice." 

In mathematics, we regard all number as increasing 
and decreasing from zero. This may be indicated by a 
diagram: 

_ to 98763432101 2345 6 789 10 , 

Similarly, if our language were theoretically perfect, we 
should have the means of expressing regularly ascending and 
descending grades of quality and quantity. But, as has 
already been remarked, even the regular grammatical com- 
parison does not indicate the remoteness from the positive 
of the upper and lower superlatives, nor does the compara- 
tive intei-vene midway. All that we know is that the upper 
comparative is the positive with an indefinite increment, and 
the superlative is the comparative with the same or a differ- 
ent increment. The same is true on the descending side, 
except that the iiio'ciuciit becomes a decrement. This may 
be partially shown by a diagram : 



NoTE. — The possible extension and the narrowing of meaning are 
shown by dots in the principal line, and the vagueness of degree is 
denoted by dots breaking the degree lines. 

To denote, with slightly more definiteness, the numerous 
possible grades or degrees of quality or quantity, an indefi- 
nite number of adverbial words, phrases, and clauses are 
employed to modify the positive. Examples follow; 



PEDAGOGICS OF GRAMMAR. 



23 



^Vord^ 



Phrases. 



Clauses. 



j slightly, so»!t'7i'/ici/, tolerably, noticrably, ) . 

\ 7'i'ry, decidedly, unusually, exceedingly, f ' 

[ to a degree, in fact, luithout doubt, in souie j 

j measure, ivithout qualification, in general ( , ff i 

] estimation, by common consent, in the high- 



i est degree, etc., 

\ if he gai)is by it. ii'hen he has an audience. 1 
where charity is descri'ed, as his means per- 
mit, since he came to the city, 10 hen a strong [^ charitable. 
appeal is made, after he became •'wealthy , ij 
the object be worthy, etc.. 



These illustrations will make clear to the student how slight 
is the service we get from the grammatical comparison when 
we take into consideration the limitless possibilities available 
otherwise. They show, too, how difficult it is to say exactly 
what we mean; and they suggest the extreme importance of 
carefully choosing our adjectives so as not to exaggerate 
or to understate our meaning. He is, perhaps, a wise man 
that uses few adjectives in his spoken and written thought; 
he will, at least, be less frequently misunderstood and 
misquoted. 



33. Extremes and Means Among- Words. — A valu- 
able and most interesting line of language work for the 
classroom can be made of what has already been given. But 
there are some exercises even more valuable, which we pro- 
ceed to explain. 

There are many adjectives that have opposites, such as 
Jiot and cold, good SinCi bad, right and wrong, ivJiitc and black. 
Between these opposites or antonyms, there frequently 
belong terms expressing a mean or average of the extremes, 
just as is the inean or average of -j- G and — G. The 
comparative degree, is, more or less nearly a mean 
between the positive and the superlative; but this mean 
is generally an inflected form of the positive. It is here 
intended that the antonyms and their mean shall be 
different words. Some examples follow to show what is 
meant : 



34 PEDAGOGICvS OF GRAMMAR. S 4 



Antonyms. 


Mean. 


+ Antonyms. 


tigly. 


fail", 


pi-etty. 


worst, 


medium. 


best, 


deficient, 


enough. 


excessive. 


cold, 


equable. 


hot. 


black, 


neutral. 


white. 


slow, 


moderate, 


fast. 


hate. 


indifference. 


love, 


small. 


average. 


large. 


antipathy, 


apathy, 


sympathy. 


sadness. 


equanimity. 


gladness. 



It will be noticed that in this exercise we may use verbs, 
as adva)iCL\ halt, retreat ; adverbs, as slowly, moderately, 
rapidly ; prepositions, as a dove, on, beloic-^aW these in addi- 
tion to nonns and adjectives. The teacher can give one set 
of extremes and require the pupil to find the other set, and 
to find later both the other set and the mean. The require- 
ment may be added that each word alone, or the antonyms, 
or all three, shall be properly used in sentences. 

34. Serial Adjectives. — vSeveral words, nearly synony- 
mous, may often be found that are antonyms of several 
others, and, between these two sets, may be a set of means. 
The task of arranging all the words in proper degree of 
quality from the lower extreme to the upper will be inter- 
esting, and generally somewhat difficult. For example, let 
it be required to arrange in this way the following adjectives 
relating to temperature, and to point out those that relate 
only to physical heat and cold, and those that have been 
transferred to ideal uses, as to personal manner, mental 
state, speech, etc. : frigid, hot, torrid, tepid, cold, lukewarm, 
coldish, fervent, warm, warmish, chilly, coolish, ardent, 
heated, freccifig, sultry, cool. 

The following words are all used in speaking of successful 
endeavor; let it be required to arrange them in order, and 
to find the nearest antonym of each : elated, Joyful, jubilant, 
triumpJiant, rejoiced, pleased, exalted, delighted, charmed, 
glad, happy, hilarious, satisfied, joyous. 

It need scarcely be stated that exercises like the last are 



PEDAGOGICS OF GRAMMAR. 



25 



to be used only in classes quite well advanced. For a supply 
of words approximately synonymous the teacher should be 
provided with works like Roget's "Thesaurus" or Crabbe's 
" Synonyms." 

35. Antonyms "by Prefixes. — In the work suggested 
above, opposition of meaning should, if possible, be expressed 
by words of different form and derivation. It is of course 
important that the pupil shall be able to give antonyms by 
using prefixes, for sometimes there is no other way; but the 
value of these exercises is much enhanced by finding those 
of different forms, and discriminating them. vSome exam- 
ples of antonyms formed by means of prefixes are sane and 
insane, absent a.n(\. pi'esent, advantaj^e and disadvantag-e, ful- 
filled and ujifulfilled, contented and discontented, intelligent 
and juiintelligent. While the discipline sought by studying 
the shades of meaning among words is of the highest value, 
almost equally profitable is it to know the exact meaning 
and effect of prefixes and sufifixes. For purposes of refer- 
ence, the accompanying tables will be found useful. 

AX(U.O-SAXOX PREFIXES. 



Prefix. 


Meaning. 


Examples. 


A 


on, at, to, in. 


aboard, abed, afield, afoam. 


Be 


at, by, for, over, to, upon. 


betimes, betide, bespeak, between. 


Counter 


against, opposite. 


counterpoise, counterbalance. 


For 


from. 


forlorn, forswear, forbid, forbear. 


Fore 


before. 


foreknow, foretell, foremast. 


Half 


one of two equal parts. 


half-dime, half-starved, half-told. 


Mis 


wrong, ill. 


mistake, mischance, mishap. 


Over 


beyond, excess. 


overpaid, overpower, overall, 
overawe. 


Out 


excess, exterior. 


outvote, output, outside, outrun. 


Self 


very, one's own. 


selfsame, selfish, self-made. 


Un 


not, contrary, reverse. 


unkind, undo, untruth, unmake. 


Under 


inferior, insufficient, below. 


undergrowth, underpay, under- 
sheriff. 


Up 


ascent, elevation. 


upheave, upland, uphold, upon. 


With 


against, from, back. 


withstand, withdraw, withhold. 



26 



PEDAGOGICvS OF GRAMMAR. 



§4 



LATIN PREFIXES. 



Prefix. 



A 

Ad 

Ante 
Circum 

Con 

Contra 

Dis or di 

Ex or e 

Extra 
In 

Inter 
Intro 

Ob 

Per 

Post 

Pre 

Pro 

Preter 



Modified Forms 



ab, abs 

ac, af, al, an, 
ap, as, at 



CO, col, 
com, cor 

contro 

away, apart 



il, im, ir 



oc, of, op 



Meaning. 



Examples. 



from, 
away. 

to, at, 
towards. 

before, 
fore. 

about, 
around. 

together, 
with. 

counter, 
against. 



out. 

beyond, 

out of. 
in, into, 

upon, 
in between, 

between, 
in, inwards, 

within. 

against. 

through, 

by, very, 
after. 

before. 

for, forth, 
forwards. 

by, beyond. 



avert, absent, 

abstract, abduct, 
advert, accept, 

affront, aHude, 

annex, assert, attend, 
antepenult, anteniundane, 

antecedent, antenuptial, 
circumvent, circumscribe, 

circumstance, circumference, 
conceive, cogent, 

collate, compel, 

corrode, collide. 

contradict, controvert. 

discern, divert, 

dispose, distract, 
expel, eject, evanescent, 

extract, event, 
extra-judicial, 

extravagant, extraordinary, 
intrude, illusion, 

impress, irregular, 
interrupt, intersect, 

interview, intermit, 
introduce, introspect, 

introvert, introflection. 
obtrude, occur, 

oflfend, oppose, 
pervert, permit, peroxide, 

perfervid, peroration, 
postpone, postscript, 
prevision, prepare, 

pretend, prelude. 

propose, propel, project. 

preternatural, pretermit, 
preter-human. 



§4 



PEDAGOGICS OF GRAMMAR. 



27 



LATIiS" PREFIXES— a7«//«W(f. 



Prefix. 


Modified Forms. 


Meaning. 


Examples. 


Re 




again, back. 


return, repel, 
resist, reset. 


Retro 




back, back- 
wards. 


retrospect, retroact, 
retrograde, retrocede. 


Se 




apart, aside. 


secede, secure, 
seclude, seduce. 


Semi 




half. 


semicolon, semicircle, 
semiannual, semilunar. 


Sub 


suf, sug, sup, 
sur, sus 


under, up. 


subscribe, submit, suffice, 

suggest, suppose, surrogate, 
sustain. 


Subter 




beneath. 


subterfuge, subterranean. 


Super 




above, over. 


superfine, supensede,- 

super-sensitive, superstitions. 


Trans 


tran, tra 


beyond, 
over. 


transpose, transgress, 
traduce, transpire. 



(iHKKK IMJKFIXl 



Prefix. 


Meaning. 


Examples. 


A or an 


privation, without, 


anemia, anarchy, anonymous, atom. 


Amphi 


two, doul)le, 


amphibious, amphitheater. 


Anti or ant 


against, 


anti-Christ, antithesis, antipodes, 
antipathy, antonym. 


Apo or apii 


fnjm, away, 


apostrophe, aphelion, apologv, 
aphorism. 


Dia 


tlirough, 


diagonal, diameter, dialogue. 


Epi or e2)h 


upon, 


epitaph, epidemic, epigram, ephem- 
eral. 


Hemi 


half. 


hemisphere, hemicrania. 


Hyper 


over, 


hypercritical, hyjaerbole. 


Hypo 


under, 


hypothesis, hypotenuse, hypodermic. 


Meta 


bevond, over. 


metaphysics, metonymy, metamor- 
phosis, metathesis. 


Para 


against, beside, 


paragraph, paradox, parody. 


Peri 


around, 


periphery, perimeter, pei'iod. 


Syn, svm, 




svntax, sympathy, 


syl, sy 


together, 


syllable, syzygy. 



28 PEDAGOGICS OF GRAMMAR. § 4 

36. Forms of the Comparative and Superlative. 

The grammars direct us to form the ascending degrees of 
monosyllables by annexing -cr and -est to the positive, and 
to observe the same rule with words of two syllables if they 
end in %v or j', or if they have the accent on the last syllable ; 
as ivisi\ tuiscr, ^uiscst; lovely, lovelier, loveliest ; narroiv, nar- 
rozvcr, narroivcst ; complete, completer, completest. But, 
as is frequent in poetry, when the adjective is placed after 
the noun, or is used in the predicate, more and most, and less 
and least are frequently used with monosyllabic nouns. 

" A form more fair, or a iace 7nore sweet, 
Ne'er hath it been my lot to meet." 

*' He is less loise btit more apt than his brother." 

Many authors, among whom Carlyle may be specially 
noted, frequently use the regular comparison for polysylla- 
bles, with inuch harshness of sound resulting; as fright- 
ful, frightfuler, frightfnlest ; beautiful, bcautifuler, beau- 
tifulest. 

The safe rule is that -cr and -est are preferable to ;//6';v and 
most when euphony will permit, but offense to the ear is to 
be regarded as a sufficient reason for rejecting the regular 
comparison. 

Strictly, words having a negative prefix are not compara- 
ble. Such are impossible, inconceivable, uiideceivable, apa- 
thetic, anonymous, etc., but such words are frecpiently found 
compared in the works of good writers. 

Many of our early writers used double comparatives and 
superlatives, and while it is regarded as bad taste to change 
these forms in our modern editions of their works, the use of 
these doubles is now obsolete. No sensible person, quoting 
Milton or Shakespeare, ventures to harmonize their language 
with modern usage, but he continues to say vtost unkindest, 
most particularest with Shakespeare, and virtuousest, 
famousest, secretest with Milton. The teacher does not need 
to be reminded that each age has its own literary laws and 
usages, and that writers of one period cannot assume to pro- 
nounce upon the taste of another. Language is a thing of 
growth, development, evolution. 



§ 4 PEDAGOGICS OF GRAMMAR. 29 

THE VERB. 

37. Preliminary Remarks. — The verb is the most per- 
plexing of all the parts of speech. No other has been so 
much discussed and so variously treated. As is the case with 
all difficult subjects, each additional effort to clear up its in- 
tricacies has served to involve matters only the more, and to 
leave the student in a worse condition of doubt and bewil- 
derment. Each writer on the subject adds new technical 
terms to the multitude of those already in use, devises a set 
altogether novel, or rejecting in part or wholly the old terms, 
introduces what he supposes to be English equivalents. The 
necessary consequence is that grammar is badly taught, 
and is not understood as a coherent scientific whole even by 
our best teachers and scholars. With each change of text- 
books, our children must learn a new set of technical terms, 
and a teacher finds, with each change of locality, that he 
must adjust to new conditions his method of treating the 
verb. 

Most of our trouble arises from the fact that writers on 
the subject have tried to adapt to our English verb the treat- 
ment employed with the Latin and the Greek. They have 
proceeded with our language, which is practically without 
inflection, precisely as if it were highly inflected, and the 
result has been a bad misfit. It is now too late to come 
forward with a scheme of treatment suited to the genius of 
our language. Many such have been olTered during the last 
decade, and while some of them have been far better than 
the cumbrous machinery of the old, all have been rejected. 
This is owing partly to an inborn conservatism and partly 
to an unwillingness to do again a work that we suppose has 
already been sufficiently done. 

38. What Is Here Proposed. — It might seem hopeless 
to attempt to extract, from all this confusion, a coherent plan 
of treatment of this part of speech — a plan helpful to the 
teacher, and capable of rendering the subject more easily 
understood by the pupil. It is certain, however, that no 
one has ever furnished a generally acceptable treatment of 



30 PEDAGOGICS OF GRAMMAR. § 4 

the verb, and no one will probably ever be able to do so. 
The writer's aim is to select from the multitude of plans that 
have been offered for studying the verb such parts as seem 
to him capable of forming the simplest and most workable 
whole. The central purpose is to furnish an outline of work 
that shall commend itself to the teacher as being- available 
for practical use in the classroom, and as simple as the 
subject admits. 

29. Deflnitioii of the A'erb. — At the very outset, we 
encounter a difficulty that seems to be insurmountable — to 
define the verb. Our language contains no word with the 
fourfold meaning of declaring, qiicstioiiijig, commanding or 
entreating, and ivishing ; yet in all these ways does the verb 
contribute to the expression of thought. The terms, predi- 
cate, tell, affirm, deny, assert, say, state, declare, and several 
others, have been employed by different writers in defining 
the verb. Many of these definitions might be quoted, but 
the result would be only to confuse the student, and to make 
clear that a definition that really defines is simply impossi- 
ble. One of our latest and best dictionaries defines the term 
as follows: 

A verb is that part of speech which asserts, declares, or 
predicates something. 

It is obvious that to use three words so nearly synonymous 
as asserts, declares, and predicates does not help us out of the 
difficulty; and besides, the question, the command, and the 
Mdsh are not provided for in this attempt at a definition; for 
no one would say that a question is an assertion, or that a 
command is a declaration. 

Perhaps the nearest approach to a satisfactory description — 
not definition — of the exact function of this part of speech is 
the following, taken with some modification from one of our 
best authorities on grammar: 

A verb is a word used to predicate something of its subject: 

1. 'Qj affirming; as, John .wtc.s- wood. Henry ?jr a scholar. 

2. By expressing a question ; as. Does John saiv wood ? 
Is Henry a scholar ? 



§ 4 PEDAGOGICS OF GRAMMAR. 31 

3. By cxp?-cssiiig a coimnaiid or an entreaty; as, Study 
your lesson. Pity the sorrows of a poor old man. 

4. By denoting a zvish ; as, JVonId that I i^'ere a boy 
again. iMay he soon conic. 

It may be observed that verbs of loishing- are usually 
included under 3 above, but it is obvious that they express 
neither commands nor entreaties. 

The following quotation from Cobbett's excellent grammar 
is given, in the belief that it will be helpful to the student: 

"Grammarians appear to have been at a loss to discover a suitable 
appellation for this important ckissof words, or part of speech; for the 
word verb means nothing more than ivord. ****** The truth 
is that there are so many properties and circumstances, so many and 
such different powers and functions belonging to this part of speech 
that the mind of man is unable to bring the whole of them into any 
short and precise description. The first grammar that I ever looked 
into told me that a verb is a word that signifies to do, to be, or to 
SiifTer. What was I to understand from this laconic account .' 

"Verbs express all the different actions and movements of all crea- 
tures and of all things, whether alive or dead. As, for insti.nce, to 
spra/c, to baric, to grow, to molder, to crack, to critmble, and tlie like. 
In all these cases there is mo7>eincnt clearly understood. But in the cases 
of to tliinic, to reflect, to remember, to lilie, to detest, and in an infinite 
number of [other] cases, the movement is not so easily perceived. Yet 
these are all verbs, and they do indeed express movemetits that we 
attribute to the mind, or to the Iieart. But what shall we say in the 
cases of to sit, to sleep, to rot, and the like ? Still these are all verbs. 

" Verbs are, then, a class of words, the use of which is to express 
the actions, the movements, and tlie state or manner of being, of all 
creatures and things, whether animate or inanimate. In speaking 
with reference to a man, to figtit is an action ; to reflect is a move- 
ment; to sit is a state of being." 

To the foregoing may be added the following from 
Brown's "Grammar of English Grammars": 

" So various have been the views of our grammarians respecting this 
complex and most important part of speech, that almost everything 
contained in any theory or distribution of the English verbs may be 
considered a matter of opinion and of dispute. Nay, the essential 
nature of a verb, in universal grammar, has never yet been determined 
by any received definition that can be considered unobjectionable. 
The greatest and most acute philologists confess that a faultless defini- 
tion of this part of speech is difficult, if not impossible to be formed." 



32 PEDAGOGICS OF GRAMMAR. § 4 

But while it is, perhaps, impossible to give briefly and 
exactly a definition of this part of speech, it is easy to rec- 
ognize the verb when we meet it in a sentence; and when 
all is said, that is the most important matter. In an exam- 
ination in gi'ammar, almost any of the definitions that have 
been formulated would be acceptable, and this is true merely 
because of their great number and confusing variety. 



CLASSIFICATION OF VERBS. 

30. Ileg:iilai' and Irreg'iilar Verbs. — The simplest 
form of a verb is that by means of which we ordinarily 
express present action, being, or state; as, I lovc\ lualk, seem. 
So far as English verbs can be said to have roots, this is the 
root form. In other tiine forms, the root or 23resent form is 
generall}' changed. In some cases the change is a suffix ; in 
others, an entirely new word is employed. But all verbs 
are arranged in two classes, 7'egular verbs and irregular 
verbs. These two classes are determined by the way in 
which certain time forms are made from the present. The 
number of these forms, or principal parts, is not the same in 
all authors; most making three, others /(3//r, and a few, Jive. 
The three tmie forms or tenses usually given as principal 
parts are: 

1 . The present; as, I see, go, work, skip, sit, sleep, seem, 
am. 

2. The past indefinite; as, I saio, went, worked, skipped, 
sat, slept, seemed, was. This tense has been variously named 
imperfect, preterit, past, first past, first preterit, etc. It 
denotes action, being, or state in the indefinite past — a year, 
a month, a day, ago. If the student understands the mean- 
ing intended, the naine is of little consequence. 

3. The perfect participle. This is the form used after 
I Jiave in the following: 

seen, gone, worked, skipped, 



I have A , , , 

sat, slept, seemed, been. 

A verb is regular if it forms its past indefinite tense and 



sent Tense. 


Past Indefinite. 


Ft 


-rfeei Partieiplt 


turn, 


turned. 




turned. 


snap, 


snap[p]ed, 




snap[p]ed. . 


live, 


lived. 




lived. 


steady, 


steadied. 




steadied. 


parley. 


parleyed. 




parleyed. 



§ 4 PEDAGOGICS OF GRAMMAR. 33 

W.'s, perfect participle by adding -d or -cd to its present or root 
form. The rules of spelling- must be observed in changing 
the present tense into the other forms. 



Principal 
Parts. 



The inflection in -ing, called the present, or imperfect, 
participle, is very cominonly included as the fourth among 
the principal parts; as, turn, tiiniiitg, turned, turned; sec, 
seeing, sazi', seen; go, going, luent, gone; etc. 

A verb is irregular if it forms its principal parts in any 
other way than by adding -d or -cd to the present. 

Present. Past Initefinite. Perfect Participle. 

( sing, sang, sung. 

I grow, grew, grown. 

Priuc-ipal I ^ , '^ , , * 1 

- speak, spoke or spake, spoken. 

Parts. 1 / r / 

freeze, troze, trozen. 

[ swim, swam or swum, swum. 

31. Verbs ^He^vly Coined Are Always Regular. — 

The regular verbs comprise nearly all in the language, and 
their number is constantly increasing. Human progress is 
marked by new methods, needs, processes, products. For 
example, the introduction of electricity as an industrial force 
has created a need for many new verbs. Greater precision 
in scientific and mechanical processes, increased exactness in 
classification, — these and many other things are adding to 
the list of verbs. The additions, however, are all regular 
verbs. It Avould be difficult to find an irregular verb that 
has come to us during the last half-century. 

Another source of increase of the stock of regular verbs is 
in the fact that we may form verbs from almost any part of 
speech; as, "Things animate and inanimate are Jid d and 
slicd in the German language." "They tlicc'd and thou'd 
me beyond endurance." "After c?/^-///j'?V/^'' about it for some 
time, she accepted the situation." 

It is, however, from the noun and the adjective that verbs 



34 PEDAGOGICS OF GRAMMAR. § 4 

are mostly formed. Thus, from the nouns ;//<?//, sJiip, key, 
lock, raft, book, head, ej'e, inoutJi, we say man the ship, sJiip 
the goods, lock the door, raft the lumber, etc. From the 
adjectives rough, sad, glad, red, sharp, etc. , verbs ending 
in -en are formed ; and from legal, moral, verbal, special, etc. , 
come the verbs legalize, moralize, etc. 

While verbs are readily and actually formed from other 
parts of speech, as indicated above, few of them become 
permanent additions to our stock of words; and it is to be 
noted that it is in bad taste for a speaker or a writer to make 
new words when there are approved terms that will equally 
well express the required meaning. But whether verbs 
newly coined are permanently added to the language, or 
whether they fall into disuse and are speedily forgotten, 
they are in ever}^ case regular verbs. 

32. Remarks on the Irregular Terbs. — In our own 

language, and in many other languages, the irregular verbs 
are the most important, for the reason that they are more 
frequently used than are the regular verbs. Moreover, our 
errors in speech consist largely in the misuse of these verbs. 
Our language contains about two hundred of them, and of 
these about GO per cent, are in daily use in every depart- 
ment of life. They are the first verbs that as children we 
learn to use, and the last that we learn to use correctly. 
The commonest and most important physical and mental 
moveinents are expressed by irregular verbs; as, see, hear, 
feel, think, knoiv, go, come, sing, begin, sit, set, lie, bring, 
take, sleep, rise, icake, run, speak, tell, gii'c, lurite, read, 
buy, sell, do, eat, drink, find, lose, ring, shine, etc. 

The mental effect produced by these verbs is the most 
vivid that the mind is capable of receiving, and this is due 
to our long and intimate acquaintance with them. Most of 
them may be displaced by less familiar and longer equiva- 
lents, l)ut the force upon the mind is much diminished. 
The student will readily feel this loss of significant effect by 
substituting imbibe for drink, proceed for go, appropriate for 
take, narrate or communicate for tell. 



§4 PEDAGOGICS OF GRAMMAR. 35 

33. Redundant Verbs. — Many verbs have two sets of 
principal parts, one set regttlar and the other irregular; as, 
beseech, besoiigJit or beseee/wd, besought or beseeched; c/othe, 
clothed or chid, clothed or clad; spill, spilled or spilt, spilled 
or spilt. vSuch verbs are redundant. The number of redun- 
dant verbs is being reduced by one of the sets becoming 
obsolete. Thus, we used to have past indefinites and per- 
fect participles bm-sf and bursted, bent and bended, ground 
or grinded, heated or het, split or splitted, and many others. 
Of these, bursted, bended, grinded, het, and splitted are no 
longer used. The tendency is to retain the irregular form, 
perhaps because it is the more expressive. 

34, Defective Verbs. — A few verbs called defective are 
used only as presents and past indefinites, and they have 
their formation />;'<'^//Arr. They are: 



Can, 


Could. 


Shall, 


vShould. 


May, 


Might. 


Will, 


Would. 


Methinks, 


Methought. 


Quoth, 


Quoth. 


Must, 


Must. (?) 


Wis, 


Wist. 


Ought, 


Ought. (?) 


Wit, 


Wot. 



Whether must and ought can properly be used as past 
indefinites is disputed. Wis, wist, and icot are old forms and 
are nearly obsolete. Beware is used only as a present form. 

35. Verbs Active-Transitive, .Vctive-Intransitive, 
and ISTeviter. — Most verbs express action or movement of 
some kind, real or ideal: physical, mental, moral, emotional, 
indtistrial, social, political; as, walk, think, sin, hate, iveave, 
entertain, elect. All such verbs belong to the great class of 
active verbs, a class comprising perhaps 09 per cent, of all 
English verbs. In a sense to be explained hereafter, all 
verbs express action. 

In any act there may be two principal elements, or there may 
be three, and even four. When there are two, they denote 
\.\\Q actor z.\\<\ the act performed; as, "• Snow falls.'' "The 
boy runs. " "The industrious boy rises early in the morning." 

If there be three principal elements, they denote the actor, 
the act performed, and the thing directly affected by the act; 



36 PEDAGOGICS OF GRAMMAR. § 4 

as, "The sun melts the snoiv.'" " Mai'y %vas]icd Wiq dishes." 
^"T\\Q far vier gave food to the hungry traveler." 

When, as in the first case, the action affects only the 
actor, the verb is intransitive, from the Latin /;/, not, and 
transire, to pass over. 

If the action expressed by the verb passes over from the 
actor to an object directly affected by the action, the verb is 
transitive. 

Transitive verbs are of two kinds, active and passive. In 
the first, the subject of the verb denotes the actor; as, " John 
struck William. " 

In the second class, the subject of the verb denotes the 
receiver of the action; as, "William was struck by John." 
These two forms of a transitive verb are called by many 
authors tlie active voice and the passive voice. In the second 
form, the subject of the verb denotes the person or the thing- 
that endures, or suffers from, the action. The word passive 
is here used in the sense of suffer from the Latin adjective 
passivus, suffering. 

8(5. Omitted Elements. — Strictly speaking, a verb to be 
transitive should be accompanied by the other two elements, 
the name of the actor and of the receiver of the action. But 
sometimes only the verb with one of the other elements, or 
the verb alone is given. This arises from one of two causes: 

1. The missing element inay be clearly implied; as, 
"John struck (object) and (actor) hurt his playmate;" 
ia.stead of, "John struck his playmate and he hurt him." 

2. The missing element may be unnecessary to the 
thought. Indeed, this is generally true of the passive form. 



Active 



f "(Sub.) Strike (obj.)! till your last armed foe expires." 

! " One sows (obj.), another reaps (obj.)." 

1 "Mary washed (obj.) and (sub.) combed (obj.)." 

[ " Men build (obj.) and time destroys (obj.)." 



" He was struck (actor)." 
" America was discovered (actor) in 1492." 
Passive ->, " The story was related (actor) with much effect." 

I "Many ancient kingdoms were established (actor), but 
[^ (receiver) were soon destroyed (actor)." 



§ 4 PEDAGOGICS OF GRAMMAR. 87 

3T. Otliei* Transitive Forms. — There are several other 
cases in wliich verbs may be used as active and passive: 

1. Where there are four elements,— the three already 
mentioned and an indirect object. 

Active. — " They gave him food." 
Passive. — " Food was given him by them." 

2. When an intransitive verb is made transitive by com- 
ponnding it with a preposition. 

" He taug/icd c\i her." 

" She was laughed at by him." 

3. When the speaker's own mind seems to be the actor 
implied. 

" I am decided to do it." " He was bent on leaving." " I am pleased 
to learn, etc." "He is inclined {disposed, resoli'cd, deter ruined, 
gricTed, pained) to make the concession." 

38. Wlieii a Verl) Is to lie Tlegarded as Transitive. — 

There is much difficitlty in deciding when a verb is to be 
regarded as transitive. If we are to be guided entirely by 
7ise, a verb is transitive only when all the elements, actor, 
verb, and receiver of the action are denoted. When, however, 
the verb expresses a command, the subject is nearly always 
missing, and is generally unnecessary. vSuch verbs are 
clearly transitive if accompanied by an object; if they 
have no object, the verb is used intransitively. 

[ " Reap (object) where you have sowed (object)." 
Intransitive \ " If he would prosper, the farmer must plow, sow, reap, 
and gather into his barn." 



Transitive 



J " Earn money and save it." 

[" Understand and practice economy. 



When two or more verbs have the same object, it is u.sually 
expressed but once, and the verbs are transitive. 

" The king jaursued, captured, tortured, and then sold, the fugitives 
into slavery." 

In cases where the object is unimportant or unknown, the 
verb should be regfarded as used intransitively. 



38 PEDAGOGICS OF GRAMMAR. § 4 

" Idleness and inactivity enervate, industry strengthens." 
"The Romans gained and the Carthaginians lost, in the struggle 
that followed." 

If the verb is in the passive, it is transitive, for only transi- 
tive verbs can have the passive form. 

"Year after year new stars are discovered, and most of them are 
catalogued." 

"The times are changed and we are changed with them." 

"The Roman Empire was rapidly dismembered and its supremacy 
among the powers of the woi-ld was utterly destroyed." 

" The ship was for a time becalmed ; later, she was driven upon a lee 
shore, where she was wrecked, and the crew was drowned." 

39. IVeiiter A'evbs. — The term iiaitcr, as used here, is 
to characterize such verbs as are //^////^I'r active-transitive nor 
active-intransitive, or, as many authors intend, neither active 
nor passive. Of these, there is perhaps none, or there are 
very few, that do not express some kind of action. Indeed, 
it may be doubted whether there is any state or condition of 
being that is wholly without either real or ideal activity; for 
molecular motion or action is just as real as the motion of 
sensible masses. The verb be is usually taken as the best 
type of a neuter verb, and yet life or existence — mere 
being — is intal activity: when this form of action ceases, the 
result is death. This is quickly followed by intense chcviical 
action^ called decay, or dccovipositio)i. 

Grammarians have tried in vain to draw a hard and fast 
line between verbs active and verbs neuter. No stich divi- 
sion can be made — no such line can be drawn. The truth is 
that all verbs may be separated into three more or less 
definite groups. 

1. Verbs that affirm or deny action real or ideal, — predi- 
cate action, — and besides, imply a state or condition. In this 
class, action is the prominent consideration, and the implied 
state is neglected. Thus, " The earth ;//('T'r.s-." " The man 
ti'orks." " Cataline hates. " Here there are the acts and the 
implied states of uiovi)ig\ of icorking, and of hating. We 
think of the act and neglect the state. These are strictly 
active verbs. 



§ 4 PEDAGOGICS OF GRAMMAR. 39 

2. Verbs that predicate state and imply action. In this 
class, it is the state that engages the attention, while the 
implied action may not even be considered. Thus, 

"He is." "God li7'cs." "The city of Troy was."' "He seems, 
appears, Aw/\s-, sick." "A'tv/ still." '' Remain (\\x\ei." 

This class includes verbs that distinctly and imquestion- 
ably express action, but the action is neglected, and only the 
state is regarded. Thus, 

"Open your eyes H'/V/c." " SAut the door //i,'///." "Sit and 7i'a/i 
erect." "The package arri^'cd safe." "The sun s /lines I) rig /it." 
" He acts sic/c." " He stands stitt." 

Here we think of the state of the eyes and the door after 
the acts of opening and shutting have been finished ; of the 
state or position of the body rt'?^r//;^ the acts; of tlie condition 
of the package after the act of arriving; and so on. These 
are neuter verbs, when thus used, because the action 
expressed or iinplied is not considered, the attention being 
wholly devoted to the state or condition of the subject. 

3. Verbs in which the action and the state are of nearly 
equal prominence. With such verbs the speaker may use an 
adverb to modify the action expressed, or he may use an 
adjective to show that he is thinking particularly of the .y/rt/r, 
or he may use both an adverb and an adjective — the one to 
modify the action and the other to denote the state. 

" The laoy acts insane." "He ixci'A Jootis/i/y." " The player acts 
graeefittty." 

" How sioeet the moonlight sleeps." 

" He looks anery." " lie ];>;)ks - r - at his ruined hopes." 

•^ ' ( sa/f \ ^ 

" We keep (pen all night." 

" How siceet the moonlight sleeps upon //lis tmn/:." 

(iii/ivrd) 

" The sunlight fell /ii>t (upon t/ie soui/iern s/opes)." 

{adivi-b) 

"The politician blew /lot and eo/d (in /lis address)." 

(adverb) 

" The door is locked -< '' ', \ at nis^/it." 
\ securely \ i^,,j^„.ri,) 



40 PEDAGOGICS OF GRAMMAR. § 4 

40. Remarks on the Foregoing Classification. — The 

student will notice that in the foregoing the impossibility of 
dividing all verbs into two classes is recognized, and that he 
is called upon to decide whether, in a doubtful case, it is better 
to modify by an adverb the meaning of the verb, or by an 
adjective to denote the state, or to do both. The advantage 
derivable arises from the fact that a difficulty distinctly for- 
mulated is often a difficulty mastered. This classification 
should lead to the banishment from our speech of such mon- 
strosities as "I feel badly," " She looks sploiduily,'" "The 
lake \iQS placidlv," "The babe lies iiuioccntly in its cradle," 
"The boarder sleeps noisy," " I am nicely, thank you." 

Although, doubtless, all verbs express some greater or less 
degree of action, it is not intended to formulate a new classi- 
fication of verbs. The truth is that there are already too 
many. The object is only to impress upon the student that 
the grammar of the English verb is a matter for the exercise 
of his best and most deliberate judgment; that no subject is 
better for the discipline of his powers of discrimination, and 
of analysis and classification. The fact that no two authori- 
ties agree in their treatment of the verb should excuse him 
for insisting upon thinking for himself. vShould he fail to do 
this, he will miss, in large measure, the culture derivable 
from the studjA of grammar, 

41. The Term "Active" as Used in Grammar. — 

Much confusion has arisen in grammar from the twofold 
sense in which the term active is used. The first meaning is 
that in which verbs are active and passive — denoting the 
I'clation of the subject of the verb to the action expressed; the 
second, where some verbs, whether they are active or passive, 
are called active because they denote actio)/, in contrast with 
others called neuter. 

Active and Passive. — " The sun warms the earth." " The earth is 
ivari)U'd\)y the sun." 

Active and Neuter. — " ]o\\n studies^ '• The child ?> pretty." 
The student will do well, when he meets or uses the word 



§ 4 PEDAGOGICS OF GRAMMAR. 41 

active, to decide in which of these two senses it is to be 
understood. 

43. Brill Witli Irrej>uliir Verbs. — It has been stated 
that most of our errors of speech come from a misuse of the 
irregular verbs. The best practical way in which to remedy 
this state of things is by frequent C'nr/ drills ; for it is by 
Jiearing the correct forms, not once or twice, but many 
times, that we learn to use them. It is not by studying 
grammar that we learn to speak in conformity with its rules 
and principles, but by Jiearing i/iitc/i, reading niucli, and 
speaking niucli. No teacher should imagine that he has 
taught the verb well unless his pupils can give the principal 
parts of all the irregular verbs in common use. In addition, 
they should be persistently exercised in such drill work as is 
indicated below: 

Si(bjccts. Principal Parts. Coinploncnts. 

I 1 

We 

He -^ r my work carefully, 

gl^e 1 1^^^ I I the best I can (could). 

They ' ^1°' ^"^^y have [- done \ my work this morning. 
I); had I the task yesterday. 

Henry [the example many times. 

The girls 

The foregoing will suggest what should be written on the 
blackboard for any irregular verb. The pupil should be 
required to make a complete statement with each subject 
when the verb form and the complement are indicated by 
the teacher. Later, the statement may be converted into a 
q nest ion. Thus, 

" /do Diy work carefully." " We do our work carefully." " Hr does 
/lis work carefully." Etc. 

" Do I do my work carefully ?" " Do we do our work carefully ?" 
" Does he etc.?" 

The progressive statement and the progressive question 
may constitute a third and a fotirth variety of exercise. 
Thus, 

" I am doing etc." " We are doing etc." 
" Am I doing the best I can ?" Etc. 



42 PEDAGOGICS OF GRAMMAR. § 4 

By turning- the same drills into the negative form and 
abbreviating, we get a much needed drill with /';// not doing, 
I don't do, He doesn't do, He isn't doing. The question with 
not naturally follows. Thus, 

" Am (not ain't) I not doing ?" " Don't I do ?" " Doesn't he do ?" 
Etc. "Didn't he do ?" " Hasn't he done ?" " Haven't they done ?" 

The drill with is and is not, isn't, aren't, and that with the 
confusing varieties of the verb to be, furni.sh excellent and 
profitable discipline. 

Of course the teacher will change the complements and 
the verbs as occasion demands. 

Another drill that should not be neglected is that with 

pronouns in the predicate. It is as follows: 

I call. 

It 1 is, be, was, were, ( I, we, he, "1 „ 

)■ < V that •! calls. 
If it J had been \ she, it, they j ^^^^ ^ 



called. 



Here the sentences in full will be : 



" It is I that calls," "It was we that called," "If it had been she 
that called," etc. 

The same drill may be made negative, and either declara- 
tive or interrogative — with and without abbreviation. 

43, A Daily Work. — The foregoing drills should find 
a place in every day's work; they may, with proper modi- 
fication, be introduced early in the school history of pupils; 
and with profit be made to cover several years. 

By actual trial in the classroom, they have proved to be a 
source of unfailing delight to the pupils. One of the notable 
results of their use is that the children soon introduce addi- 
tional verb forms from their drills into their daily conversa- 
tion. If the student will notice closely the tenses used by 
children and uneducated people, he will be surprised at their 
limited number. 

If there is 2i practical ^\de of grammar, if in addition to its 
disciplinary value, it is to teach us "how to speak and write 
the English language correctly, " or at least, more correctly 
than formerly, it is realized by these drills, and others that 
may be devised by the ingenious teacher. 



§ 4 PEDAGOGICS OF GRAMMAR. 43 

MOBES OF VERBS. 

44. Preliminary Remarks. — There are several modes 
or ways in which verbs may be used in predicating. By 
predication is meant every form or use of the verb in 
asserting or denying action or state, in making inquiries^ in 
expressing eoniniands or entreaties^ and in merely assuming 
action or state. Authorities differ much, and doubtless will 
continue to differ, about the number of modes and their 
definitions. The number generally given is five; the indica- 
tive, the potential, the imperative, the suhjuneti-ve, and the 
infinitive. Many authors insist that the English verb has 
only three modes; the indicative, the imperative, and the 
subjunctive. The reasons usually given for rejecting the 
potential and the infinitive modes will be noticed later, but, 
in teaching the subject of modes, no great harm can come 
from regarding them as five in number. 

45. Predicatiiis' Action or Merely Assiimino- It. — 

Before entering upon the consideration of the several modes, 
it is necessary that the student should imderstand exactly 
what is meant by the terms predicating and assuming with 
respect to the action or the state expressed by verbs. 

The word from which predicate is derived is prcedicarc, 
and the meaning of this Latin word is to cry out in public, 
to proclaim. As used in grammar, predicate includes all the 
functions of the verb and its various complements. These 
uses are for the purposes of affirming ox denying, questioning, 
commanding, wishing, etc. Such uses constitute only par- 
tially what we mean hy predication. Another form of predi- 
cation arises when the action or the state is only taken for 
granted or assumed. Thus, we may .say 

The boy escaped by running. 

Here there are two forms of action, one asserted — escaped — 
and one assumed — running. We do not assert, say, declare, 
that the boy ran ; biit we use language from which the act of 
running is implied — it must be understood or assumed. 

Even when a word derived from a verb is used as an 



44 PEDAGOGICS OF GRAMMAR. § 4 

adjective to modify a noun, there is an obvious assumption 
of action, although grammarians content themselves with 
calling it a verbal adjective. Thus, a ritimiug brook, a 
sleeping child. 

Some other forms of the verb predicate by assuming the 
action. These will be considered later. 

4:6. The Indicative Mode. — ^The form or use of a verb 
by means of which we affirm or deny a simple fact or ask a 
question, is the indicative mode of the verb. This word 
indicate really means to point out, show, or declare, although 
it is applied to the use of qnestioning or inquiring; and in 
grammar we often find that the use of a term is thus carried 
beyond its exact meaning. Examples to illustrate the indic- 
ative mode are the following: 

" James ^<7^^ to school." " Z><;t'jr James ^^t^ to school?" "James is 
not a studious boy." 

"Harry went to the brook." '' Ha^'c the birds not gone south?" 
" Will you not visit tis? " 

47. The Potential Mode.— There are some short verb 
forms called auxiliary or helping verb.s. These are much 
■used with other verbs, and they help to make what many 
grammarians call verb phrases. The student will notice that, 
in the sentences given above, several of the verbs have 
double forms; as, does go, have gone, etc. These compound 
forms are verb phrases. They may be taken apart, and each 
part considered separately with respect to its functions; or, 
as most grammarians prefer, they may be treated as if they 
were simple forms. 

The different forms regarded as being in the potential 
mode are all verb phrases. The auxiliary words by means 
of which we may recognize this mode are may, can, must, 
might, could., tvould, and should. When we meet verb 
phrases containing any of these words, we may be sure that 
they are in the potential mode. 

The indicative and the potential modes are the only modes 
by means of which we are able to express questions; but 



§ 4 PEDAGOGICS OF GRAMMAR. 45 

while the indicative mode, used for this purpose, inquires 
only about mere facts, the potential is employed to make 
statements and to ask questions about the ability, necessity, 
duty, etc. of some person or thing to do or be something or 
other. Thus, He can read. She may go. Should he obey ? 
Must he recite ? He might be late. 

The name potential is derived from the Latin word 
potentia, which denotes power or ability. Among the 
auxiliaries given above, can and could are the only ones that 
have this meaning; so that the mode is named from these two 
words, and its meaning is made to include all the other help- 
ing words of this mode of the verb ; as, may, must, might, etc. 

48. Fuuctions of the Several Modes. — Every mode 
has some prominent function or use, and it is of great 
importance to the student that he shall know in each case 
what this function is. For the indicative mode, the act 
itself and the time of its performance are the matters of 
leading import. "The sun shines." "The sun shone.''' 
"Spring has come.'" " The day w/// soon dazun." '■'■Have 
the enemy retreated f " Here the form of the verb makes 
the time of the act very distinct. In the potential mode, the 
time of the act is of little concern — indeed, it is scarcely 
taken into account. For the times denoted by He may come 
and He might come differ scarcely at all, and the same may 
be said of He may Jiave come and He might have come. In 
all these cases the time of the action expressed by the verb is 
very vague and uncertain. It is what is intended by the 
word potential that is to be thought of as prominent — the 
probability, etc. of the act. The first forms, so far as they 
denote any time, point to the future, and the others to the 
past; and with this limitation, all are wholly indefinite as to 
time. He can read predicates only ability that may have 
extended far into the past, and may extend into the indefinite 
future. Having premised this, we give the following: 

Definition.— The potential mode is tliat form or use of 
a verb by which action is predicated as possible, necessary, 
permitted, or obligatory. 



46 PEDAGOGICvS OF GRAMMAR. § 4 

It should be added that many authors reject this mode, 
and regard the auxiharies as principal verbs in the indica- 
tive mode, followed by infinitives; as, I can (to) go. I might 
(to) come. I may (to) have come. This view would make 
can, might, and may transitive, each having as its object an 
infinitive used as a verbal noun. 

49. The Imperative Mode. — The imperative mode 

is that form or use of a verb in which the predication takes 
the form of a command, an entreaty, or an earnest request; 
as, ^'Go thou and do likewise." ^'■Remember thy Creator." 

Since the person commanded is generally addressed 
directly, this fonn of the verb has its subject in the second 
person singular or plural, and usually omits it. There are, 
however, instances in which this is not so; as, "Now tread 
%ve a measure. " Now move %ue on." "Come wc that are 
loyal to the king." " Laugh tJiose who can, weep tliose who 
may," 

If the student will read again what is given a few para- 
graphs back to the effect that each mode has some leadhig 
function or use, and if he will examine the use of the verb 
in the imperative luode, he will see that the time of the 
action is entirely indefinite, unless denoted by the context. 
It is the command that is most important. If it is desired 
that the time at which the action is to be performed shall be 
known, adverbial modifiers must be added to the predicate. 

"Honor thy father and thy mother." (Constantly.) (While you 
live.) 

It may be added that since commanded action can be 
obeyed only after the command has been given, the time of 
the imperative reaches from the early to the far fttture. 

50. The Stihjtinctive Mode, — The treatment of the 
subjunctive mode is difficult, not merely on account of the 
nice points involved, but also because grammarians have 
failed to agree upon what the mode includes. This mode gets 
its name from snbjiinctivus, subjoined— joined in an inferior 
or subordinate relation to something else. The implication 



§ 4 PEDAGOGICS OF GRAMMAR. 47 

is that the subjunctive mode is used in subordinate clauses. 
We cannot, therefore, with this kind of clause alone, make 
a complete statement, or express a question or a command. 
Thus, 

" Were the earth as heavy as the sun, etc." " If a man 'ii>c7-c twenty- 
feet in stature, etc." " Unless the moon be utterly destroyed, etc." 

When we read such clauses, the mind demands something 
to be added that may complete the sense. This something 
is, in each case, a main or principal clatise. Thus, 

" Were the earth as /leai'y as t/ie su/i, a man could not stand erect." 

The fact is that we may find in subordinate clauses all the 
tense forms of the indicative and potential modes, and some 
other forms not belonging to either of these modes. The 
subordinate character of such clauses is generally shown by, 
certain conjunctions denoting doubt, condition, uncertainty, 
contingency; as, if, though, idi/css, providing, save, except, etc. 
To illustrate, we may say, 

If I am, be, was, were, sJiall be, Jun'e been, had been, shall have 
been, etc. 

Unless I may be, might be, may have been, might have been, etc. 
E.xccpt lie go, goes, went, were going, may go, may be going, etc. 

The foregoing forms are only a small part of those that 
may be met with in subordinate clauses. This fact has led 
to a great variety of opinion as to the forms that shotild be 
called subjunctive. What tense forms should be excluded 
as not subjunctive, and what admitted ? No one has so far 
been able to answer acceptably, or to construct a definition 
of this mode that will clear away doubt. 

Undoubtedly the easiest solution would be to call them all 
subjunctive if they occur in subordinate clauses, or else banish 
the mode from our grammars. But to this choice of the one 
or the other extreme few will accede, and no one has found 
a satisfactory mean. 

51. Definition of tlie Siibjnnetive Mode. — A defini- 
tion of this mode as formerly used — as we meet it in reading 
the old writers — would run nearly as follows: 



48 PEDAGOGICS OF GRAMMAR. § 4 

Definition. — The subjunctive mode of a verb is the 
form or use of it that, in subordinate predication, expresses 
doubt ^ contingencj', zoish. or a mere supposiiioii that may or 
inay not end in fact. 

Doubt. — ''If he be a gentleman, he will remove his hat when he 
enters." 

Contingency. — "If I were he, I should obey the order." 
Wish. — " I would my daughter were dead at my foot, and the jewels 
in her ear." " Would she were mine." 

Supposition.— "//"///t- sky fat t, we shall catch sparrows." 

Professor Meiklejohn says, "The subjunctive mode has for 
some years been gradually dying out. Few writers, and still 
fewer speakers, use it. ***** g^^^ ^ knowledge of 
the uses of the subjunctive mode is necessary to enable us to 
understand English prose and verse [written] anterior to the 
present generation. Even so late as the year 1817, Jane 
Austen, one of the best prose writers of this century, used 
the subjunctive mode in almost every dependent clause. 
Not only does she use it after z/and though, but after such 
conjunctions as ////, until, because, and others." 

The writer believes, however, that this mode is still much 
in use, especially in our best newspapers and magazines, but 
in speech much less than formerly. It would be a pity if the 
many nice distinctions and shades of meaning, and the added 
variety of sentential structure made possible by the subjunc- 
tive mode, should be lost from our language. 

53. Kno>vledge of the Subjunctive Mode That 
Teachers Should Have. — In the classroom the materials 
dealt with in teaching grammar are: 

1. Current speech. 

2. Extracts from early aud from modern writers. 

With respect to these two classes of matter, that of current 
speech is not much considered in grammar work. The same 
may be said of the works of the latest writers. It is largely 
with selections from the earlier classical authors that the 
teacher deals. What is called "the best usage" is largely 
determined by what these have done. Milton's writings, the 



§ -t PEDAGOGICS OF GRAMMAR. 49 

plays of Shakespeare, the tales and poems of Scott, — the 
works, in short, of nearly all the authors from whom we get 
our selections for use in teaching- grammar — abound in the 
subjunctive mode. This mode is, indeed, "dying out," but 
not from the teacher's work. 

Moreover, the principal need for grammar in our education 
is to enable us to understand what we read. And what better 
reading can we have than the writings that, after the test of 
time, the world calls classical .^ Hence, the teacher, more 
than any other person, should know not only what is, but also 
what was, the usage with regard to this form of the verb. And 
no harm will follow if the pupil comes to imagine that what 
was once so commonly used is still current. Even though he 
should employ it in his own speech, and in what he might 
write, it is an embellishment the continuance of which should 
be encouraged rather than otherwise. Its effect is like that of 
some of the Greek particles that clearly imply whole sentences. 

53. Examples of tlie Subjunctive Mode. — For the 

purpose of illustrating the earlier and the present forms 
and uses of the subjunctive mode, we give the following 
quotations : 

" Unless he /la^w wings, he cannot ascend the peak." 

" If a man die, shall he live again ?" 

" Though he slay me, yet will I trust in him." 

" Would that night or Blucher were come." 

" O, had I the wings of a dove, 

How soon would I taste you again." 
" O, that those lips /z^ZiY language." 
"What if thine heaven be overcast ? 

The dark appearance will not last; 
Expect a brighter sky." 
" If wishes were horses, beggars might ride." 
' ' We could catch fish were the river dried tip." 

" The world would be better did men hwe as strongly as they hate." 
" I would we could hear tidings of our jolly chaplain." 
" 'I were [were = s/unildbe—\n^\c2Cvi\Q mode) right sorry for it,' 
said the Knight of the Fetterlock, ' if he were lost.' " 
" If he have been killed, the world will profit." 

• Unless he act unjustly, my wealth will be restored." 

• Might he but come, I should be happy." 



50 PEDAGOGICS OF GRAMMAR. § 4 

" Though this be madness, yet there is method in't." 
"Yet, though the ebbing of Time's mighty river 
Leave our young blossoms to die, 
Let him roll smooth in his current forever, 
Till the last pebble is dry." 
"Yet, unless we greatly err, this subject is distasteful to most 
readers." 

"If disastrous war should sweep our commerce from the ocean, 
another generation may renew it; if it exhaust our treasury, future 
industry may replenish it ; if it desolate and lay waste our fields, still, 
under a new cultivation, they will grow green again, and ripen to future 
harvests. It were but a trifle even if the wall of yonder Capitol were 
to crumble, if its lofty pillars should fall, and its gorgeous decorations 
be all covered by the dust of the valley." 

54. Remarks I'pon tlie Foregoing. — The student 
should examine and carefully compare the above quotations, 
and should determine which italicized verbs ought no longer 
to be considered as in the subjunctive mode. The last 
example, which is from an oration by Daniel Webster, fur- 
nishes a striking abundance of subjoined clauses containing 
verbs in the subjunctive mode. Is there not proof here that 
this mode is not really dying out ? 

The student will see that the distinguishing function of 
the subjunctive mode is to express mere contingencies and 
conditions that are generally true when taken with their 
opposite jneanings. Any verb so used is in the subjunctive 
mode, as it is now understood by the niajority of writers on 
English grammar. 

55. Siilyimctive Mode Has but Vague Reference to 
Time. — The student should carefully note that it is the con- 
tingency, the doubt, the mere fiction, that dominates in the 
subjunctive mode, and that the idea of time is almost 
entirely neglected. Such indications of time as in any case 
may happen to be, must be inferred from the sentence as a 
whole. Thus, in 

" If it rain, I shall not go," 

we see that raiii, while present in form is future in fact. 
Similarly, in the sentence, 
" If I were he, I should not yield," 



§ 4 PEDAGOGICS OF GRAMMAR. 51 

the sense requires lis to regard tvcrc as present, although 
in parsing we call it past. So that what are called tenses 
are, in this mode, only varieties of form without much signifi- 
cance of time. Such as there is, usually points to the 
future, sometimes to the present or to the past, and often 
covers all time. 

56. Tlie Infinitive Mode. — There is no special diffi- 
culty in this mode, although it has been treated in a variety 
of ways. vSome authors, notably during the last twenty 
years, have classed as infinitives what are usually called 
participles, because both are unlimited. By this it is meant 
that they undergo no changes to accommodate themselves 
to changes in the person and number of subject words. The 
implication is that the other modes, called _/?////i', are changed 
in soine or all of their tenses when changes are made in 
the person and number of their subjects. This, however, 
happens in only a few cases. Thus, in the indicative pres- 
ent we have only two changes, or cases in which the form of 
the verb is limited. 

1 1^'ork, thou 7tvr/^est, he luorks^ zee work, you icork., they 
luork. 

There was formerly he zcorketh.^ but that is now obsolete. 

With the infinitive there is no such change; whence its 
name. 

Some other authors have called both infinitives and parti- 
ciples by the name of verbals. But there is really no good 
reason for thus merging them into one class, for while they 
are much alike in function they are very different in form. 
The terms gerund and gerundive, lately imported from the 
Latin, and complicated with the obsolete distinction between 
the Anglo-Saxon dative and the infinitive proper, serve only 
to confuse both pupil and teacher. The writer would urge 
in this matter that the old method of treatment is the sim- 
plest and best, and that we should continue to use the terms 
infinitive Q.n6. participle in their usual senses. 

57. Subject of tlie Infinitive. — There is heard much 
discussion among teachers as to whether or not the infinitive 



52 PEDAGOGICS OF GRAMMAR. § 4 

has a subject. After all is said, the fact remains that action 
implies an actor; every verb, in whatever mode, has a sub- 
ject expressed or implied; even participles, inasmuch as 
they have the verb function, imply a subject. But infini- 
tives and participles omit their subjects so frequently, and 
besides take on so strongly the nature of the other parts of 
speech that inost grammarians omit notice of a subject. 

In the sentence. They told him to go, hint is just as much 
the subject of to go as they is of told. He zcas told to go, 
really means //r was told {Jiiiii) to go. When Hamlet says, 
To be or not to be, he is thinking of the desirability of life, 
and his meaning in full is [Man) to be, or [man) not to be. 
They /promised me to come is in full, They promised me to 
come [themselves], or [tJieni) to come. 

A few grammarians have said that when the action denoted 
by both an infinitive and a finite verb is performed by 
the same person or thing, then the subject of the infinitive 
is in the nominative case. The following are illustrations: 

" I expected to go to New York." 

" He was ordered to resign," 

" They refused to obey the officer." 

This, however, is clearly erroneous; for, if in the first 
sentence /is the subject of to go, then it should be correct to 
Avrite " I expected / to go to New York, " "I expected ^//r 
to go," " I expected tJicy to go, etc. " But we cannot say " I 
expected lie to go," " He asked / to go ": in all such cases 
we must use the objective forms of the pronoun. From the 
fact, then, that whenever the subject of the infinitive is 
expressed, it is in the objective case, we must infer that 
when it is only understood, it must be in the same case also, 
if it be supplied. 

The old rule of grammar, " The subject of a finite verb 
is in the nominative case,'' implies that there are verbs 7iot 
finite, wnth subjects that are not in the nominative case. 
The Latin rule, ^'■The subject of an infinitive is in the accu- 
sative,'' might have as its English equivalent, " The subject 
of an infinitive is in the objective case," for objective and 
accusative are equivalent terms. 



§ 4 PEDAGOGICS OF GRAMMAR. 53 

5S. Tlie Sign of the Infinitive. — The little word /o is 
by most writers called the si^yi of the infinitive, although it 
is often omitted. It is by some authorities regarded as a 
/yarf of the infinitive, and by others, as merely 2^ prcpositioi. 
The bulk of authority seems to be in favor of the latter 
view, but strenuous arguments have been urged on each 
side. 

Perhaps no word in the language has been more written 
about than this so called "sign of the infinitive." It has 
been called a preposition^ an adverb, a prefix, a particle, an 
auxiliary, a little u>ord, a sign of the infinitive, a. part of the 
infi)iitive, etc. These refinements about so small a matter 
have little practical value, nevertheless the writer is tempted 
to call attention to the likeness between this use of the word 
and its more common use as a preposition. 

It is primarily the function of a preposition to bring into 
relation words having no obvious connection. 

the house — the river 
the horse — the soldier 
kind — animals 
walked — water 

These unrelated words may be brought into relation by 
inserting between them in order by, near, to, into ; and by a 
variety of other prepositions the relation may be varied. 
Thus, we may use beside, ivith, towards, through. 

Now this is just what is done by to with the infinitive and 
some other word : 

ready — oblige 
orders — leave 
mean — go 

Still, the writer thinks it is of little consequence whether 
to be regarded as a preposition or as a part of the infinitive. 
The former is perhaps more nearly in consonance with the 
true function of the word. 

59. The Sign ''•'I'o'" llesyarded as a Preposition. — If 

to is a. preposition^ then the infinitive is always a verbal noun. 



54 PEDAGOGICS OF GRAMMAR. § 4 

object of the preposition, and the preposition connects it 
with some other word and brings the two words into rela- 
tion. Thus, 

" We desire to excel." 

Here to connects desire with the verbal noun excel and 
brings the two words into relation. Excel is the object of 
to, and to excel is then a }ioiiii pJirase in the objective case 
after desire. 

Take another sentence : 

" He received bread to eat." (Here to cat ^^ for eating.') 

In this sentence, to connects bread and the verbal noun 
eat., and forms with it the adjective phrase to eat, and this 
phrase is a modifier of the noun bread. Again, 

" He tried to rescue the drowning boy." 

The phrase to rescue is an adverbial modifier of tried, and, 
more widely, rescue, with its modified object, forms, with 
the preposition to, the completed adverbial modifier of tried. 

Such cases as "To be contents his natural desire," are 
explained by supplying the missing subject of the infinitive. 
Thus, {Him) to be, etc. The preposition to, in this construc- 
tion, connects him and be, and the infinitive be is a verbal 
noun. 

60. The Sign " To " as Part of tlie Influitive.— If to 

is regarded as a part of the infinitive, and is to be supplied 
when missing, then the verb with its sign may become, 

1. A iioim used in the nominative or the objective case. 

" To toil is his necessity; his relief is to rest.'' 
" The enemy decided to retreat." 

2. An adjective or an adverb. 

" He asked for work to do." 

" The boy is quick to understand." 

The closeness of the connection between to and the verbal 
word is evidenced by the dictiiui of the critics that the two 
words should never be separated by an interposed word. 
Thus, they insist that we should say to annihilate utterly or 
utterly to annihilate rather than to utterly annihilate. 



§ 4 PEDAGOGICS OF GRAMMAR. 55 

It must be conceded, however, that their contention has 
not been observed more than it has been ignored, in the 
practice of good writers, for the "split infinitive," as it is 
called, is of very frequent occurrence. 

61. Complements of tlie lufliiitive. — ^ Although the 
infinitive is in a large sense an abstract noun, it still retains 
its character as a verb, and may, therefore, be modified by 
an adverb, or take adjective, noun, and pronoun comple- 
ments, just as is the case with verbs in other modes; as, to 
choose zvisely, to be careful, to appear sick, to act the gentle- 
man, to deserve punish jneiit, to resemble him. 

G'^. The Time Denoted 1).t the Infinitive. — In the use 

of the infinitive, it is not the purpose to denote the time of an 
action, but simply to speak of action in the abstract. As has 
been explained above, it is, when considered apart from the 
preposition to, nothing more than a verbal noun; although, 
when taken in connection with to, it may become an adjec- 
tive or adverbial phrase. If the idea of the time of the 
action is to be added, it must be done by other words. 
Goold Brown says : ' ' What is called the present infinitive can 
scarcely be said to express any particular time. It is usually 
dependent on another verb, and therefore relative in time." 
Dr. Blair remarks: "The infinitive mode carries neither 
time nor ai^rmation." 

THE PARTICIPLES. 

63. Similarity of the Participle and the Infinitive. 

As has been said, the participle is very similar, in some of 
its fiinctions, to the infinitive. This is especially so when 
the preposition to is regarded as a part of the infinitive; for 
then the verb is used as a noun, as an adjective, or as an 
adverb. The participle is not usually treated as a mode of 
verbs, although, as we have seen, it is sometimes classed 
with the infinitive, forming one group called the infinitive 
mode, and sometimes both forms are called 7'erbals. In the 
sense that it is not changed on account of any change in the 



56 PEDAGOGICvS OF GRAMMAR. § 4 

person and number of the subject, it is infinitive — iinlimited. 
But owing to the fact that the presence of its subject is less 
frequent and less important than is the case with the infini- 
tive proper, it is thought better to treat it separately. 

Like the infinitive, it predicates by assigning, not affirm- 
ing, action or state ; and, like the infinitive, it may be mod- 
ified by an adverb, may take a subject or an object, or may 
be followed by a predicate adjective or by a predicate noun. 
" Waking car/y, we set out at once to ascend the peak." 
"The boy, being indolent, gradually fell behind his class." 
" Horatio, being a scholar, spoke to the ghost." 
''Having accumulated a large fortune, he returned home." 

The participles have been by some authors regarded as 
forming -a participial mode, but the objection to this is obvi- 
ous. For if the participle is to be considered as having mode, 
there seems to be no reason why it cannot be merged in the 
infinitive mode, as has been done by many grammatical 
authorities. 

64. Classification of Participles. — As is the case with 
every other form of the verb, there have been innumerable 
classifications made of the participle. To enumerate even a 
portion of these, without discussing them, would serve only 
to confuse the student and to profit him not at all. These 
classes have tense names, although it must not be understood 
that the indication of time by the participle is definite or 
important. As is true of all verb forms except the indicative 
mode, time must be denoted, if at all, by accoinpanying 
words. This is exemplified in the following sentences: 

" Being deceived has the effect of rendering one suspicious." 

The action expressed by the verbals may be referred to 
any time whatever. 

'' Having been defeated, 2iXi able commander should become more 
wary, indeed, but more determined to win." 

Here the time of the participle may be present, past, or 
future. The sentence expresses a universal truth. 

The following classification is the one most commonly 
accepted; 



§i 



PEDAGOGICS OF GRAMMAR. 



57 



tabijE of participi^es. 



Names. 


Transitive- 
Active. 


Transitive- 
Passive. 


Intransitive. 


Neuter. 


Present. 


loving. 


being loved. 


fly. 


being. 


Past. 


loved. 


loved. 


flown. 


been. 


Perfect. 


having loved. 


having been 


having flown. 


having been. 


Perf. Pro- 


having been 


loved. 


having been 




gressive. 


loving. 




flying. 





65. Remarks. — The past participles, active and neuter, 
are rarely found except in verb phrases, a use that some 
verbs seem to admit. It would be difficult to construct a 
sentence containing loved used by itself as a past active par- 
ticiple, but flown may be so used correctly; as, " Tlie bird, 
flown from its nest in search of food, never returned." This 
is an authorized construction, though the perfect participle 
would be better: "The bird having flozun,"' etc. These 
participles are generally given by the grammarians, perhaps 
on account of their occasional occurrence, and because they 
are used in forming the perfect active participle. Thus, 
loved is active in having loved. 

66. Degrees of Assumed Predication of Partici- 
ples.— Predication by participles is of very many, but indefi- 
nite degrees. When they are joined directly to a noun — 
preceding it^the verbal origin of such modifiers rarely 
occurs to the mind, and they become mere adjectives; and 
such they should be called, unless their verbal nature is for 
some reason interesting. Instances are: a writing pad, 
running water, a surprising feat, a spoiled child. 

Similarly, the verbal noun often contains so little predica- 
tion that it may be regarded simply as an abstract noun. 
Thus: ''Swimming is easy to learn." "He earned his 
living by flshing." 

The predication comes out more distinctly in such uses as 
the following: 

"Columbus, fearing that his men might mutiny, made them 
promises." 



68 PEDAGOGICS OF GRAMMAR. § 4 

This is nearly equivalent to the predicating form, ' ' Colum- 
bus /.?«r^</ that his men might mutiny, and etc." The fol- 
lowing participles also, in the degree of their predication, 
approach very closely the finite verb. 

'' Having finished their lessons, the students went to their homes." 
" He was a good boy — confiding, loving, obliging." 
''Having been pdled and indulged, he became a spoiled boy." 
"He was interrupted after having been reading for an hour." 
"After having performed the operation, the surgeons were seen 
leaving the hospital." 

61. The Fixture Participle. — Some authors give forms 
that they call the future active, and the future passive, par- 
ticiples. They are, gODig to love, to be about to love, going to 
be loved, to be about to be loved. 

It seems to the writer that one might almost be warranted 
in calling an entire sentence a noun, on the groimd that it 
represents or names a thought, which is a thing, as to call 
stich collections of words partieifles. Grammar is made suf- 
ficiently farcical by taking together the long complex phrases 
of the verb, — a practice that deprives pupils of much of the 
discipline obtainable from the study. Indeed, the teacher 
does wisely to insist on determining the exact nature and 
function of the v/ords in sentences, each word by itself. 



THE te:n^ses of tekbs. 

68. Deflnitioii. — Tense is a variation in the form or use 
of verbs and of verb phrases to denote difference in the time 
and degree of completeness of the expressed action. After 
what has already been said on this subject, the student will 
understand how slightly the idea of time is denoted by tense 
forms, except in the case of the indicative mode. It is, how- 
ever, in all the modes, best to observe a uniformity of names, 
even though their signification of time varies. 

In order to prepare for a better understanding of the sub- 
ject of tense in general, the writer has thought best to 
present first the tenses of the indicative mode. The following 



§ 4 PEDAGOGICS OF GRAMMAR. 59 

diagram will be found useful in furnishing- the pupils with 
clear notions on this somewhat puzzling matter. The 
diagram should be placed on the blackboard, to be explained 
by teachers and pupils. 




SAST^PSKF. 



69. The Present Tenses. — The shaded part of the 
diagram is intended to show that the word prcsctit in . ordi- 
nary speech does not mean no^v — tliis instant. Ncnv is, as it 
were, a steadily moving mathematical point; i\ie present is a 
variable portion of time on both sides of nozu. Thus, we say 
this jninntc, today, the present month, this year, century, 
epoch, etc. To "act in the living present," human beings 
need more than this mathematical now. Strictly speaking, 
there is no present time — all being past or future. So that 
we use the word present, both in life and in grammar, some- 
what vaguely. It is relative to human tasks and experiences. 
" He is studying his lesson" means that, engaged in studying, 
he has passed, and will pass, through a considerable period. 
Some of that period is now past time; the rest of it is yet 
future time. We speak of this entire period as being in the 
present tense. There is here, however, no uncertainty as 
to its position with relation to the noic; we are uncertain 
only with respect to its extent into the past and the future. 

It may be objected that it-is the time of speaking we. mean 
when we say "He is studying his lesson." But even the 
utterance of thought consumes a time that, like that of study- 
ing, lies partly in the past and partly in the future. Human 
action has no absolute 7io%i>. Moreover, when we speak of an 
act anticipated, or recall it after it has been performed, we 
speak of it as a luhole. 



60 PEDAGOGICS OF GRAMMAR. § 4 

The meaning of the v^ord prcsoit in grammar is better seen 
in what we call the lunvcrsal pi'cscnt X.qw'&q. "The earth 
revolves. " ' ' The sun shines. " "A triangle /las three sides. " 
"Jesus is the Savior of men." The present of this use of the 
verb generally covers all finite time. 

In the use of the universal present the student should be 
careful not to employ the past for it. Thus, "Columbus 
believed that the earth teas round." "He insisted that the 
product of seven by six was forty-two." "He assured his 
audience that Jesus was the Savior of men." 

This error of speech is of extremely common oc(?Virrence. 

The student should note the distinction between / work 
and I a7n working. The first denotes habitual or cnstouiary 
action. It is the universal present applied to ordinary finite 
action. / avi working denotes vioiuentajy, eontiniioiis^ or 
temporary action. The former, / zvork, has for its present 
an extent of time ranging perhaps far into the past and the 
future, and it is therefore the present indefinite. The latter, 
I a7)i Ivor king, is called the present progressive, and usually 
involves but little time on each side of the now. 

Like the present, the present-perfeet tense is used to denote 
action of two kinds. / have thought. I have been tJiinktng. 
The former is called the prese>it -per feet indefi)nte, and it 
denotes past action completed at the present, — the time of 
speaking, — or at some time of which the present is a part. 
The latter denotes past action in progress at the time of 
speaking, and has been called the present-perfeet progressive. 

In the sentences, " vSince Virgil wrote, Rome has fallen," 
" The poems of Homer have been much admired," the shaded 
part of the diagram must, for the first sentence, be extended 
so as to include the time when Virgil wrote; for the second 
sentence, it must go still farther back, so as to begin with the 
time when Homer's poems were first admired. 

But the context may make narrow and definite the range 
of the present. " The clock has y/zj-/ struck." " The year 
1899 was pregnant with events that make history. " 

By the figure of rhetoric called Vision, the present may be 
carried by imagination into the past or the future, as we 



§ 4 PEDAGOGICS OF GRAMMAR. GI 

please. Similarly, the past or the future may be conceived 
as present. 

"The twenty-first century kas just daivned. Human progress /las 
been making great strides. The power of steam and electricity has 
been supplanted by forces hitherto unsuspected. Nature is yielding 
her secrets less reluctantly and more and more rapidly." 

" Behold poor old Socrates. He sits undejected in his prison. His 
friends Iia^'c been with him ever since his conviction and sentence." 

In such transfers of the present or any other time, the 
tense names remain imchanged. 

70. The Past Tenses. — Very similar to the tenses of the 
present are those of the past. They are two in number, the 
past tense or preterit and the past-perfect tense. Each of 
these has two forms, the i)idefinite and the. progressive. 

I /ndefi nite. — Active. — " I walked." 
Preterit i. Passive. — " He was advised." 

I Pj-ogressi7'e.^-\ci\ye. — " I was walking." 

{ Indefinite. — Active. — "He had walked." 
Past-Perkec T j Passive. — "He had been advised." 

I Progressii'e. — Active. — "He had been walking." 

The following definitions of these tenses may be useful to 
the student: 

1. The past iiidefliiite tcn.se denotes action at some 
indefinite past time. 

2. The past progressive tense denotes action /;/ progress 
at some indefinite past time. 

3. The past-perfeet indefinite tense denotes action 
completed at some indefinite past time. 

4. The past-perfeet progressive tense denotes action 
in progress at some indefinite past time. 

It is usual to call 1 and 2 simply the past tense, or the 
preterit, and 3 and 4 the past-perfect. 

71. Tlie FiTture Tenses.— There are two tenses for 
future time, the future and the future-perfect. As is the 
case with the tenses of present and of past time, each of the 
tenses of futm-e time has two forms, one for completed action 
and one for continuous ox progressive action. 



02 PEDAGOGICvS OF GRAMMAR. § 4 

Examples illustrating these forms are given below: 

I Indefinite. — Active. — " He will walk." 
Future \ Passive. — " He will be advised." 

[ Progressive. — Active. — "I shall be walking." 



Future-Perfect 



Indefinite. — Active. — " I shall have walked." 

Passive. — "He will havebeen advised." 
Progressive. — Active. — " He will have been walk- 

[ ing." 

It is a fact not generally known that in our conversation 
we use the future-perfect tense perhaps not a score of times 
during our lives, and that one may read many books and not 
meet this form of the verb once in all of them. When the 
future perfect is required, some equivalent is used. Thus, 
for "When I reach home, I shall have walked fifty miles," 
we may say, "When I reach home, it will be fifty miles that I 
have walked." It is a ten.se that must be sought in books; it 
occurs almost not at all in conversation. The practical value 
of this tense, therefore, is slight, and if it were not for the sake 
of showing completely the relations of tenses, it might be omit- 
ted as being little more than a curiosity of the English verb. 

73. Passive Proj^rressive Forms. — The student will 
notice the omission of W\q. progressive passive forms. Strictly, 
there are, and perhaps there should be, no such forms ; but 
within the last half- century, there have come into more or less 
general use z. present passive and z. past progressive pas.sive. 
' ' The house is being built. " ' ' He is being advised. " ' ' The 
house was being built." " He was being advised." 

Of course the.se are the only passive progressives that could 
be used, for no one would tolerate such forms as "He has 
been being advised," "He will be being advised," "He 
should have been being advised," etc. 

Good writers avoid altogether the use of progressive passive 
forms. 

Equally bad, and nearly as common, are the so called 
passive forms with the active participle in -ing. "The 
house is building. " "The cellar is digging." "The wood 
is sawing." 



§ 4 PEDAGOGICS OF GRAMMAR. 63 

It is better to employ a few more words, if necessary, than 
to introduce forms so questionable. We may always say 
"They [the carpenters, etc.] are building the house." 

73. Tlie Enipliatic Present and Past Tenses. — In 

addition to the foregoing tense forms, there are two others 
that are used when we wish to place special emphasis on the 
action expressed by the verb. These are Iho present and the 
preterit with do and diei. 

Present Tense. — " I ih) walk." " He docs think*." 
Past Tense. — " I did walk." " He did think." 

The progressive forms also are frequently used when we 
wish to be emphatic; in this case the stress of voice is put 
on the first verb element. Thus, " I am walking." " I ivas 
walking." " He Jias been sleeping.". 

•74. Siininiary of tlie Tenses of tlie Indicative Mode. 

It follows from the foregoing that the indicative mode has 
six tenses, comprehending fourteen tense forms. These 
tenses are the present and the present-perfeet, the past and 
t\iQ past-pe7-feet, the future and \\iQ future-perfect. 

The various tense forms may all be converted into ques- 
tions by differently arranging the subjects and predicates, 
and by using do and did when they are needed. Thus, 

I love. I am loving. Do I love ? Am I loving ? Did I love ? 

I have been seen. Have I been seen ? 

I shall have been seeing. Shall I have been seeing ? 

75. Synopses of tlie Tenses of All the Modes. 

ACTIVE VERB. — Regular and Irregular. 



TENSES. INDICATIVE MODE. 



Present 



Indefijiitc. — I walk. He writes. 

Progressive. — I am walking. He is writing. 

Perfect indcf. — I have walked. He has written. 

Perfect prog. — I have been walking. He has been writing. 

Emphatic. — I do walk. I do write. 



64 



PEDAGOGICS OF GRAMMAR. 



Past 



' Indefinite. — I walked. He wrote. 
Progressive. — I was walking. He was writing. 
Perfect indef. — I had walked. He had written. 
Perfect prog. — I had been walking. He had been writing. 
Emphatic. — I did walk. I did write. 



Future - 



Indefinite. — I shall walk. He will write. 
Progressive. — I shall be walking. He will be writing. 
Perfect indef. — I shall have walked. He will have written. 
Perfect prog. — I shall have been walking. He will have 
been writing. 



Present 



POTENTIAL MODE. 

Indefinite. — I may walk. He can write. 
Progressive. — I may be walking. He can be writing. 
Perfect indef. — I may have walked. He can have written. 
Perfect prog. — I may have been walking. He can have 
been writing. 



Past 



Indefinite. — I might walk. He could write. 
Progressi7>e. — I might be walking. He could be writing. 
Perfect indef. — I might have walked. He could have 

written. 
Perfect prog. — I might have been walking. He could have 

been writing. 



Present 



SUBJUNCTIVE MODE. 

Indefinite. — If I walk. If thou walk. If he write. 
Progressive. — If I be walking. If thou be walking. If he 

be writing. 
\_Perfect indef. — If I have walked. If he have written.] 
\_Pe7fcct prog. — If I have been walking. If he have been 

writing.] 



Past 



Indefinite. — If I walked. If thou walked. If he wrote. 

Progressive. — If I were walking. If he were writing. 

P effect indef. — If I had walked. If thou had walked. If 

he had written. 
Perfect prog. — If I had been walking. If he had been 

writing. 



PEDAGOGICS OF GRAMMAR. 



65 



Present 



IMPERATIVE MODE. 

Indefinite. — Walk [thou]. Walk [ye or you]. Write 

[thou, ye, or you]. 
Progressive. — Be [thou, ye, or you] walking. Be [thou, 

ye, or you] writing. 
Emphatic. — Do [thou, ye, or you] walk. Do [thou, ye, or 

you] be writing. 



Present 



INFIXITIVE MODE. 

f I)idefinite. — To walk. To write. 
Progressive. — To be walking. To be writing. 
Perfect indef. — To have walked. To have written. 
Perfect prog. — To have been walking. To have been 
writing. 



„ ( Walking. 

Present < „,. .^. 

( Writing. 



PARTICIPLES. 

I Indefinite. — [Walked. Written. ] 
Perfect indef. — Having written. 
Perfect prog. — Having been writing. 



Indicative 



Potential 



PASSIVE VERB.— Irregular. 

Present. — 1 am seen. 
Present-perf. — I have been seen. 
Past. — I was seen. 
Past-perf. — I had been seen. 
Future. — I shall be seen. 
Future-pcrf. — I shall have been seen. 

Present. — I may be seen. 
Present-perf. — I may have been seen. 
Past. — I might be seen. 
Past-perf. — I might have been seen. 

Subjunctive. Present. — If I be seen. Past. — If I were seen. 
Imperative, Be [thou, ye, or you] seen. 

Infinitive. Present.— To be seen. Present-perf. — To have been 
seen. 



PARTICIPLES. 

Present. — Being seen. Past. — Seen. Present-perf. — Having been seen. 



66 PEDAGOGICS OF GRAMMAR. § 4 

*7G. Auxiliary Verbs. — The following verbs are used 
as helping, or auxiliary verbs : 

Present. — do, have, shall, will, can, may, must, am, is, be. 
Past. — did, had, should, would, could, might, was. 

Some of the auxiliaries occur also as principal verbs; as, 
do, be, have, and ivill. Thus, 

•' I (/^ my work." "God is." ''Troy was." "John has a book." 
" When a woman «'///, she will." 

Besides their use as principal verbs, do and did are auxil- 
iaries of emphasis and of inquiry. Have, shall, and zvill are 
tense auxiliaries, in verb phrases the first denotes com- 
pleted action; the other two denote fjit?ire action. May, 
might, can, could, should, zuould, and must are mode auxil- 
iaries, and the several forms of be are by some authors called 
voice auxiliaries; by their aid, verb phrases are made passive. 
This is shown below: 

Active. Passive. 

He loves. He t's loved. 

He may love. He may be loved. 

He might have loved. He might have been loved. 

To see. To be seen. 

If I saw. If I luere seen. 

So far as it can be done, tlie student should write out the 
auxiliaries in their various modes and tenses, and he should 
be very familiar with the uses of each. This is especially 
important in the case of be and have. 

There are some other words that have been included 
among the auxiliaries; as, let, ought, going. 

" Let him go" has been supposed to be " Go he! " a sort 
of third person imperative present. It is, of course, only 
"[You] let him [to] go." "He ought to go" has been 
made into an obligative mode. But ought was originally 
only the past tense of oive, and it is now a defective verb. 
This sentence is really a shortened or idiomatic form of 
" He owes it (is under obligation) to go. " " He is going to 
write" some authors call the intentional mode; and Professor 
Melklejohn, as has already been seen, makes a future infini- 
tive intentional, " To be going, to love," " To be going to be 



§ 4 PEDAGOGICS OF GRAMMAR. 67 

loved." But this kind of thing serves no useful purpose, 
and should not be seriously considered. 

'7 a, "■ Shall " and " Will." — In no way can one furnish 
better evidence of being- really cultured in the English lan- 
guage than by using s/ia// and tfi// always correctly. This, 
of course, includes also their respective past forms, sJionld 
and ivonld. It might be well to note that although these are 
called the past tenses of sliall and zvill^ they usually point 
to future action. 

Much has been written upon the correct use of these words; 
but we continue to hear, and to see in print, blunders with 
respect to them. The subject is difficult, and we can hope 
to master it only by constant watchfulness of our own 
speech, and by careful reflection on the different ways in 
which, these verb forms are used by speakers and writers. 

78. Fundamental Meaning of " Shall " and "Will."" — 

Will and zvonld originally meant purpose, determination, 
strong intention. Since all these have reference to fiitiirc 
action^ the words have come to be used in promising, in 
threatening, in predicting, and iu announcing mere future 
action. Moreover, since nearly everything pertaining to the 
future is involved in more or less uncertainty, the elements 
of doubt, contingency, conditioji, have served to increase the 
difficulty. This difficulty is met with especial frequency in 
the use of shall and should. 

The sense of shall and should was originally obligation. 
That was during the early history of our language. / shall 
go originally meant, therefore, nothing more than / ought to 
go. But one is expected to do, and is likely to do volunta- 
rily, what he is under obligation to do; hence, this meaning 
is now entirely lost from shall and partially lost from should, 
and they are mainly used to express simple futurity, moral 
obligation, and often compulsion by a force from without. 
Both shall and zuill are employed besides in promising and 
threatening, and in many other ways. In most of these uses, 
there remains a greater or less degree of determination, 
resolve, intention. It is obvious that when it devolves upon 



68 PEDAGOGICS OF GRAMMAR. § 4 

words to express so many cliff cent shades and degrees of 
thought, one must expect more or less difficulty in using 
and understanding them, 

19. "Shall" and "Will" Denoting Detei-mination. — 

The rule generally given is that zvill in the first person and 
shall in the second and tliird persons denote purpose, resolu- 
tion. To this rule there are many exceptions, some of which 
will appear later. This element of determination or will 
may be: 

1. The Will of the Speaker.— 

"I will go, notwithstanding your opposition." "Be sure that we 
would go if we could." " He shall not enter without permission." 
" They shall do as they are told." " I ordered that they should not 
make an attack upon the fort." "Will I do my duty ? Of course I 
will." " I will drown, and nobody shall help me." (Resolved to 
drown, and determined to accept no help.) "We promised that we 
would do the work." "You shall digest the venom of your spleen 
though it d.o split you." " If I were you, I would not do it." " If he 
were my boy, he should obey." (On compulsion.) (From choice.) 

The speaker may desire to weaken the Ti.'/// element, and may 
finallygetso farinthatdirectionas to indicate nothing stronger 
Ihaxi preference^ inclination, desire. If preference is indicated 
by other words in the sentence, we have such cases as: 

"I &)\o\.\\6. prefer to remain at home." " You would be glad to see 
him, I have no doubt." " They should be delighted with their pres- 
ents." " I shall come ivith pleasure." " You would oblige me much 
by attending to the matter." "I should rather be excused from 
attending." " I should (or would) as soon live as die." "If I had the 
power, 1 should compel \i\vs\ to resign." 

Again, the speaker's will may rest in the statement of 
obligation or advantage. In this case, the determining will 
or condition operates from without — it is external compul- 
sion, opportunity, or favoring conditions. 

"You should be kind to your mother." " They should make large 
profits by the transaction." " I should go, but I cannot spare the 
time." "You should see him at your earliest convenience." "The 
crops should be unusually good this season." " It should rain today." 

There is a form of speech, known as the language of offi- 
cial courtesy.^ employed by officials in conveying orders to 



§ 4 PEDAGOGICS OF GRAMMAR. G9 

their subordinates. It relieves the superior from the embar- 
rassment of seeming to give orders, and the subordinate 
from that of receiving them. 

"You 7iiill carry this message to the admiral, and he zuill inform you 
as to your future movements." " The soldiers of the army will main- 
tain the strictest vigilance, and they will yield perfect obedience to 
their officers." 

2. The Will of the Hearer. — The usual form in this case 
is that of inqiiir}' concerning the hearer's judgment or pref- 
erence, or his will towards the speaker, or towards some third 
person. It may take the form, also, of a statement concern- 
ing the will of the hearer. 

" Shall we go now ? " " Should they be admitted?" " Would you 
do evil that good may come?" "Will you have him arrested?" 
" Shall he come into your office ? " "Should I tell him that you are 
not at home?" "Shall I call tomorrow?" "You promised that 
they should obey." "You would do it, and must take the conse- 
quences." " O, you will, you rascal?" "Would you promise to do 
otherwise ?" 

The will of anotlier may be inquired about, or a statement 
made about it, in the third person. 

" Will Mr. A be good enough to hear what the bearer has to say ? 
If Mr. A would help in this matter, he siiould not hesitate to ask a 
similar favor from the writer, his friend." 

3. The Will of the Person Mentioned.— 

" When a woman will she will, and that's the end o't." " He would, 
but dares not." "How often would they have gone back, but they 
could not." " Will he do it; dare he do it ? " " Would he do the serv- 
ice for money ? " 

This form of willing weakens until finally it is only cus- 
tomary aetion. 

" He would lie on his back for hours, watching the clouds." " The 
swallows would disappear when autumn came." " He would go for a 
walk every morning before breakfast, and they would lie in bed as long 
as possible." " They will always fly their kites when there is wind." 
" Why will he weary the good people with his chatter ?" 

4. TJic Will of a Higher Pozcer, or Nature, or Mere 
Chance. — For the operations of nature or of an imagined 
higher power, the Latins employed a personal subject where 



70 PEDAGOGICS OF GRAMMAR. § 4 

we use the pronoun it; as, "Jupiter will rain rain to- 
morrow." "Jove thunders." "Ceres will increase our 
harvest." 

There has been much discussion as to whether we should 
say, "It should seem, appear, etc.," or "It would seem, 
appear, etc." Neither expression denotes or implies any of 
the determination originally in luoiild, or of the obligation in 
should. Neither does either luoiild or shotild express futu- 
rity. The meaning of each is very nearly "It seems." 
After considering all the circumstances of a case we might 
say either, "It would seem, or "After all, it should seem." 
Should follows the usage of sJiall^ and zvould of tvill. Now, 
since it is correct to say, " It will seem best, I think, for you, 
etc.," and "If it shall seem best, etc.," it must be equally 
correct to say either, " It would seem," or "If it should seem. " 
The preference should perhaps be given to the former expres- 
sion, but when a conjunction denoting doubt, condition, or 
contingency precedes, should is better than would. 

"It will rain tomorrow." " If it shall come to pass." "Although 
it should be late, it would make no difference." " Should oxygen and 
nitrogen unite as readily as oxygen and hydrogen, all life would be 
destroyed from the earth." "Although the whale is a mammal and has 
lungs, it would be impossible for it to live upon land." " The weather 
should soon change for the better; doubtless it will." " If the clouds 
would only go away, we should be much more comfortable." " If the 
clouds should go away, we would be much more comfortable." "If 
the day should come when you would return, send me word." "I 
should be sorry if you should fail." "Thy rod and thy staff shall 
comfort me." " It would be strange if some one should not have visited 
this island." 

" How strange it should be that this beautiful snow 
Should fall on a sinner with nowhere to go ! 
How strange it luoiild be, when the night comes again, 
If the snow and the ice struck my desperate brain ! " 

" If he should come, I would go." " If he would come, I should go." 
" If he would pay me a fair price, I would do the work." " Unless it 
should rain, tomorrow should be a fine day for our trip ; for it is the 
month of Ma}-." 

80. "Shall" and " AVill '^ Denoting- Mere Futu- 
rity. — The announcement of future action may be : 



§ 4 PEDAGOGICS OF GRAMMAR. 71 

1. A Merc Predict io)i, or an Inquiry as to Future Action. — 

" He will come tomorrow." " You will surely be detected." "The 
time will pass rapidly." "Even though he should apologize, I would 
(or should) never forgive him." " If he should fail to accomplish the 
undertaking, he will be disappointed." " He would be disappointed if 
he should fail to accomplish the undertaking." " I shall be there on 
time." " When shall we three meet again?" " If you should come to 
the city, you will call to see me, will you not?" " Shall you go to the 
theater tonight?" "Will your father go, or shall you go instead?" 
" He insisted that I should have confidence that, sooner or later, he 
would pay me." " Shall you not be glad to go ? " "I should be very 
glad." "Shouldn't we be delighted?" "If they should come, would 
(or should) 3'ou be glad?" "Shall not my mother depend upon her 



The student will notice that, in the foregoing' .sentences, 
while futitre action is the conspicuous element, some of them 
express in a greater or less measure contingency, ^uill, etc. 
Indeed, it is difficult to avoid blending these various mean- 
ings. In this lies the necessity for considering carefully 
what we would say and how we should say it in each case. 

Careful consideration is needed in cases where futurity, 
ivill, and obligation are combined in various measures. The 
principal difficulty in the use of these attxiliaries is found in 
such combinations. 

" What would you do, and what should I do, in such an emergency?" 
" What should you do, and what would he do, in that case ?" " How 
shall I repay you for what you will suffer in my behalf ?" " How will 
(or shall) he repay you for what you will (or shall) suffer by going to 
the army in his place?" " If he would do such a thing, he should be 
punished." "If twenty cents will pay for five oranges, how much 
should be paid for three oranges ?" "At that rate, how much would 
(or should) iouv oranges cost?" "How many shall I get for eight 
cents ? " " How much shall I earn in three days, at four dollars a day? " 
" How much shall I pay for the coat, and what will you charge me for 
the hat?" 

2. A Promise or a Threat. — 

" He shall be punished." " Come with us and you shall (a proinise 
merely) have a good time." " Come with us and you will (simple pre- 
diction) certainly enjoy yourself." " He said that we should share the 
prize money." " They shall suffer for this." "It shall go hard with 
him." (The speaker's will.) " It will go hard with him." (Not the 



72 



PEDAGOGICS OF GRAMMAR. 



speaker, but some one else will cause it.) "He promised that they 
should be punished." "It was said that they should be punished." 
(Ambiguous ; it may mean ought to be, or were going to be, punished.) 
The same is true of the following sentence. "It was reported that 
they would be punished." (It may mean wanted to be, or %uere going 
to be, punished.) " He shall do as he is told; if not, you shall punish 
him." (The speaker's permission is granted to punish him.) " He 
shall obey ; otherwise, you will report (you are directed to report — 
official courtesy) the fact." 

81, Collections of Exami^les. — Every student shovild 
have a note book in which to record all kinds of sentences 
collected from classical sources. They are valuable not only 
for reference, but they serve to keep such matters before the 
mind. This is a condition indispensable to accurate scholar- 
ship. By readin<^ such collections aloud they sink into the 
mind throug-h the ear, so to speak, and presently the tongue 
is rebuked if its utterances are at variance with what the ear 
demands. 

Many other instances of the use oi sJiall and ivill might be 
given here, but the writer believes that the student will be 
able to supply what may be needed in addition to those above. 



TABT^E OF THE TERB. 





H 

P 



Action 
expressed 



Form 



. Use 



r ,r -.-• r Active. 

I ransitive \ 
I (^ Passive. 

j f Active. 

Intransitive i ^t <. 
[^ [_ Neuter. 

Regular — lov^e, walk. 
Irregular — go, come. 
Defective — ought. 
Redundant — dive, dream. 



Principal 



Auxiliarv 



walk, go. 
walked, went. 



I walked, gone. 

r do, may, will, have. 

j did, might, would, had. 

j be, can, shall, must. 

(_ was, could, should, 



PEDAGOGICS OF GRAMMAR. 



73 



THE ADVKRI5. 

83. Office of tlie Adverb. — In treating of the adjec- 
tive, it was stated that its function is to narrow the extension 
and enlarge the comprcluiisioii of the noun's meaning. The 
same is true of the adverb in its relation primarily to the 
verb, and secondarily, to the adjective or to another adverb. 
Thus the verb ;v/;/, used alone, may denote the act in every 
conceivable p/aee, time, manner, or other limitation — its 
extension is universal or unlimited. When a modifier is 
joined to the verb, the extension is narrowed so as to include 
the act of running only under certain limitations of time, 
place, manner, etc. 



today 

rapidly 

canjiilly 

here 

imviediatcly 



at once 
by and by 
ivitit speed 
luit/i ease 
i along t/ie river 



lohen the signal is gi^'en 
because he is frightened 
t/iat lie may escape 
ivhither he may find help 
as he ivas iftstrticted to do 

Any word, phrase, or clause used as above to modify the 
meaning of a verb, or, in other words, to enlarge its compre- 
hension and narrow its extension, is an adverb. This is 
exactly the effect upon an adjective or an adverb, when the 
meaning of either is modified by an adverb. 



today 
always 
good -> /;/ school 
for food 
extremely 



jrood 



when his father is at home 
because he was told 
where others are bad 
if he is paid fill- it 
although he might be bad 



In a similar way, it may be shown that the meaning of 
an adverb may be modified by another adverb, or by an 
adverbial phrase or clause. 



83. Adjectives and Adverbs in Tlieir Relation 
to Verbs. — This matter was treated to some extent in 



74 PEDAGOGICS OF GRAMMAR. § 4 

connection with the verb, but its importance and its relevancy 
here require a further consideration. 

It has been stated that the nature or function of an active 
verb is twofold. It expresses aetioji and asserts or implies a 
state of the subject while in that condition of action. 

The neuter verb docs little more than predicate a state of 
the subject ; as, James is sick. This verb, however, although 
it aids in the assertion, which, indeed, coiild not be made 
without it, is used to bring the subject and the attribute into 
relation. It is, therefore, a connective. For this reason, 
grammarians have called the verb is in its various forms a 
copula^ which is a Latin word meaning a connective. Hence, 
the neuter verb has two very well marked functions or 
offices: the predicating or asserting function, and the con- 
nect i)ig or copn/ative function. 

It has already been explained that every verb denotes 
action in some degree, but in this and some other verbs, 
the action is so obscure that they have been called neuter 
verbs, — neither active nor passive. Now a neuter verb, or 
mere copula, can be used in two ways only: 

1. To join a subject to an adjective or a participle deno- 
ting the state of that which the subject represents, or to an 
expression equivalent to an adjective or a participle. This is 
the predicate adjective or the participle used in the predicate. 

"The girl i.s «t-/{'." " The leaves are yrr///;/^^." " The sun is just 
now going behind the mountains." 

2. To connect a subject with a noun, a pronoun, or any 
substantive expression denoting the same person or thing as 
the siibject. This is called the predicate noun. 

"The boy is a. scholar." "It is Jie." "It was i/ic cause of your 
J ail u re.'" 

84. Neuter Verbs Cannot Be ModiflLert. — It appears, 
then, that the meaning of a pure neuter verb or of a copula 
cannot be modified by an adverb, for an adverb is used with 
verbs to denote the time, place, manner, degree, etc., of the 
action they express. Existence simply or state requires an 
adjective, not an adverb. Thus, you cannot say, ' ' He is 



§ 4 PEDAGOGICS OF GRAMMAR. To 

gladly,"' "He looks angrily,'" "He sits erectly."" Hence, 
where the modifying' word denotes only the place or the 
time of the being, or the state of the subject, it is really an 
adjective. For example, in " He is here," " She was there,"' 
"The hoy is at school,'" "I shall be where I am needed,'" 
the italicized elements must be taken as adjectives. It may 
be conceded that many grammarians and the dictionaries call 
the words here and there adverbs, and such they usually 
are; but they are sometimes adjectives. Several of our 
latest and best writers are discriminating attributes of being 
and mere state from attributes of action, making all of the 
former, adjectives. 

85. A'erbs That Are Botli Active and Xeuter. — 

Some of the verbs denoting both state and action frequently 
are accompanied by both adjectives and adverbs; the former 
denote the state of what the subject names, and the latter 
modify the meaning of the verb. 

" John lies in bed sich."' Here /// bed tells where he per- 
forms the act of lying, and sick denotes his state. 

"He sat crt'cf on-a-c/ia/r." "He lives rw/Av// in'the-ltoiiic-flf-his- 
anccsiorsy 

In the first of these two sentences, erect describes the 
attitude of the person denoted b\- he, and oii-a-chair is an 
adverbial phrase pointing out the place where the action was 
performed. The case is exactly similar in the second 
sentence. 

The distinguishing test of a neuter verb is that tJie being 
or state it denotes cannot be modified by an adverb; and in 
the case of verbs expressing both action and state, adverbial 
modifiers can be used only with reference to the actional 
function of the verb. 

It is often a nice point to determine whether we wish to 
modify the action expressed by the verb, or to modify the 
state. 

"They landed safe on the shore."" Here on the shore is 
adverbial, but many would say safely. A little thought, 
however, will make it clear that we are to think of the 



76 PEDAGOGICS OF GRAMMAR. § 4 

people or things as being safe after the aet. The sense, 
therefore,,jrequires an adjective. 

"He remained quiet, waiting for his father," or, " //^ 
remained, quietly zvaiting for his father." In the first sen- 
tence, the word and the phrase are both adjectives; in the 
second, quietly zvaiting for Jiis father is the predicate adjec- 
tive. It denotes a state and not a manner of action. More- 
over, the verbs remained differ in meaning" in the two sen- 
tences. In the first sentence the meaning is kept quiet, 
preserved a state of quietness; in the second the meaning of 
remained is stayed behind. The former is, therefore, more 
nearly a neuter verb than the latter. 

"He sat still, watching the birds." "He sat, slill ivatcJdng the birds." 

adj. adj. adj. 

" He lay on a rock dreaming of home." 

adv. adj. 

" She seemed /;/ every action rational." 
adv. adj. 

" The snow lay 07i the nor t Item hill slopes leaking away its life." 
adv. adj. 

Sometimes it is uncertain which is required, an adjective 
or an adverb. In such cases it is usual to give the preference 
to the latter. 

"He looked ifidifferent{ly) at the wonderful display." "He 
walked resoluie{ly) towards his formidable enemy." "My watch 
runs slo7v{ly)." 

86. Classification of Adverbs Accoixling to Their 
Use. — Many classifications of adverbs have been made, but 
none of them covers all the functions of this part of speech. 
The division most commonly made is into four classes, and 
these classes are determined by their use. 
1. Simple. 2. Interrogative. 3. Conjunctive. 4. Modal. 

1. A simple adverb is any word used as an ordinary 
adverb, and having no other function or use than as a modi- 
fier; as, (jO quickly, extremely careful, quite cautiously, to go 
promptly, to do his duty thoroughly. 

2. An interrogative adverb is an adverb used to ask a 
question concerning the time, manner, place, or cause of an 
action or a state. 



§ 4 PEDAGOGICS OF GRAMMAR. 77 

"IV/iy do you go?" ''U'/ic/i will he come?" ''Where are they 
going ? " ''How are you today ? " " IV/icre/ore is he here ? " 

3. A conjunctive adverb is an adverb that modifies 
like an adverb, and, like a conjunction, connects or introduces 
clauses. 

" I know a bank whereon the wild thyme grows." " You will behave 
as good children should, 1 am sure." " W'lien you go, take me with 
you." " Whither it goeth ye know not." 

Some authors say that the conjunctive adverb generally 
modifies an element in each of the connected clauses, and 
others insist that it is only the verb in the subordinate clause 
that is modified by the conjunctive adverb. The former view 
is perhaps the better. In the first sentence given above, 
bank is modified by all that follows, and groxus by zvhcrcoii. 
"I was told where he lives. " In this sentence, where he lives 
is the object of was told, and where is a modifier of lives. 

4. A niodiil adverb is an adverb that modifies the mean- 
ing of an entire sentence, or denotes how or in what degree 
its sense is to be taken. 

" He will/;v^/'^i'/''/)' come." " You will not be on time." " Are you 
going to the city ?" " Sitre/y." " He must, therefore, suffer the con- 
sequences of his act." " Hence, we may conclude that the sum of the 
angles of a triangle is equivalent to two right angles." 

Many grammarians have left it more or less doubtful as to 
what should be included in the class of modal adverbs. Per- 
haps the best means of determining whether an adverb is 
modal or not is to vary its position, and if the meaning of the 
sentence is not thereby changed, the word may be regarded 
as belonging in this class. 

" I ■&\i2ii\ perhaps go to New York." 

Here the adverb may, withotit affecting the sense, be 
placed in almost any position, a fact showing that the mean- 
ing of the entire sentence is modified by it. 

87. Resi^onsives. — Among the modal adverbs are placed 
certain words of affirjiiation ; as, jr*?, yes, surely, certainly, 
indeed, verily ; also adverbs of negation ; as, no, nay, not, 
and a few others. Most of these are regarded not as adverbs, 



78 PEDAGOGICS OF GRAMMAR. § 4 

but as abridged sentences. They resemble in function the 
interjection, but many authorities deny that such words 
belong to any part of speech. But whenever they determine 
the mode in which an entire sentence is to be taken or con- 
ceived, we should call them modal adverbs. 

88. Classification of Adverbs Aecordingf to Their 

Meaning.— Adverbs are divided into classes that denote 
time., place., degree, manner, cause, etc. 

In etymological parsing, the pupil is generally required to 
classify adverbs with reference to their meaning rather than 
to their use, but it is more satisfactory to include both func- 
tions. Thus, in the sentence, ' ' The house is cheerful when the 
children are at home," ivhen is a conjunctive adverb of time. 

89. Adverbial Objectives. — A noim in the objective 
case is often used as an adverbial modifier denoting time, 
measure, distance, weight, value, etc. 

"The clock strikes every half-Iiour." "We shall set out /oinor- 
row." (Toinorrow = on or during tomorro'iv.) "He was in college 
iowx years." " The emperor was more than six /t'c/ tall." "I do not 
care a. Jig for his opinion." "The book is worth, a do// a r." "The 
train was two liours late." " He looks like his drot/wr." 

90. Tlie Position of tlie Adverb. — The adverb should 
generally be placed immediately before an adjective or 
another adverb that it modifies, and directly after a verb 
consisting of one word, and after the first auxiliary of a 
verb phrase. The position of an adverb that modifies an 
infinitive has been much disputed about, but the bulk of 
authority is perhaps opposed to giving any word or words a 
place between the infinitive and its "sign" to. Whether 
the adverb should precede the infinitive or follow^ it is a 
matter largely depending on euphony, and on the influence 
of other words. 

"Gaily to burgeon and broadly to grow;" " carefully to observe," 
"to observe carefully;" "I asked him to decide promptly," " I asked 
him promptly to decide." 

In consequence of the careless placing of adverbs, sen- 
tences are very frequently of uncertain meaning; or they 



§ 4 PEDAGOGICS OF GRAMMAR. 79 

often have a sense entirely different from that which the 
writer intended. Perhaps more errors of this kind arise from 
the use of the word oily than from that of an}- other word in 
the language. The following sentences will exemplify the 
different senses that may be owing to difference in the posi- 
tion of only : 

"Only Harry's brother chided him" — No person except Harry's 

brother etc. 

"Harry's only brother chided him" = Harry had but one brother, 

and this brother chided 
Harry. 

"Harry's brother only chided him" = Harry's brother did noth- 
ing more than chide him. 

f "Harry's brother chided onlv him " 1 ^, , , , , • -, , 

\ ,T , , , ,.,,,.- ,,,;. = Harrys brother chided 

I "Harrys brother chided him onlv J -.. ' , , , •-, , 

^ ■ ■* Harry, and he chided 

no one else. 
A notable authority gives the following rule for placing 
only ; our reason for quoting it is that it is equally useful as 
a general rule for placing adverbs: 

" Place the only next to the word or phrase to be modified by it, 
arranging the rest of the sentence so that no word or phrase that the 
only might be regarded as modifying shall adjoin it on the other side." 



TABLK OF THE ADVERB. 



ADVERBS 



1. SiMPLK.— { 



Tiinc. — When, then, soon. 
Place. — Where, there. 
Manner. — Quickly, kindly, slowly. 
[ Degree. — Quite, very, nearly. 
Interrogative. — When? where? how? 
I 3. Modal. — Perhaps, not, certainly. 
4. Conjunctive. — Where, how, why. 
1^ 5. Adverbial Objective. — Worth a dune, rest an hour. 



THE PREPOSITION. 

91, Definitioii of the Preposition. — The preposition 
is almost the only part of speech that has been defined sub- 
stantially in the same terms by nearly all grammarians. The 
definition usuallv given is the following: 



80 PEDAGOGICS OF GRAMMAR. § 4 

" The preposition is used to connect words and show the 
relation between them." 

It should be noted, however, that any two words arranged 
with reference to their reciprocal meaning, are in relation. 
But the relational function of the preposition does not distin- 
guish this part of speech from the relative pronoun, the con- 
junctive adverb, the conjunction, or even from the copula. For 
example, the word is placed between Henry and zveary estab- 
lishes between them the relation of subject and attribute, and 
denotes that relation. Indeed, if a teacher's language be 
closely noticed, it wall appear that a very common inquiry is 
in reference to the relation between such and such words. 
There are perhaps very few words in the English language 
applied so widely and so vaguely as this word relation. 

To illustrate the exact function of this part of speech, some 
pairs of unrelated words are given below, and are then 
brought into relation by means of interposed prepositions: 
fly — house going — school 

f over 1 f into \ 



kind^ , , J- animals 



fly ■{ J" y house going { , )■ school 

i from I \h ' 

[^ tliroitgh J ytoxvards 

kind — animals 

among ^ 

witti 

towards 

\_„. 

It would, however, be difficult to improve the definition 
usually given for the preposition. 

92. Phrases.— Two or more words properly related, and 
capable of performing in a sentence the function of a single 
part of speech, form a phrase. When the phrase is intro- 
duced by a preposition, it is b. prepositiojial phrase; when by 
a participle, the phrase \s participial ; Mdien by a verb in the 
infinitive mode, it is an infinitive phrase. If the office of a 
phrase is that of an adjective, an adverb, a no7in, or a verb, 
it is respectively an adjective phrase, an adverbial phrase, a 
snbstantive or noun phrase, or a verb phrase. 



§4 PEDAGOGICS OF GRAMMAR. 81 

Adjective Phrases. — A cord of ivood, a boy ivith a basket, food for 
dinner. 

Adverbial Phrases. — Sorry to go, careful of money, strivey^r success. 

Substantive Phrase.—" To endure with patience is difficult." 

Verb Phrase. — "He should liave gone." "He could have been 
elected." 

93. Prepositions Used Adverbially. — In the matter 
of origin, the prepositions are more recent than the adverb. 
Professor Whitney says of the former that they were 
' ' created a separate part of speech by the swinging away of 
certain adverbs from apprehended relation to the verb, and 
their connection in idea with the norm cases which their 
addition to the verb had caused to be construed with it." 

Accordingly, the adverbial side of the preposition is very 
pronounced, and we constantly meet it without an accom- 
panying object. There is, however, an increasing tendency 
to give prepositional phrases in full. Thus we are more 
likely to say, "He has gone aboard the ship," "The boy 
rode around the town," or "The father walked before the 
ivagon and his son behind //, " than we are to omit the 
objects. By this transfer of adverbs the number of preposi- 
tions is steadily increasing. 

94. Governinent by Prepositions. — The term govern- 
ment has been much used in grammar to denote the power 
that some parts of speech have to compel words, in certain 
relation to them, to assume particular case forms. This is 
not true to any great extent except with regard to the case 
forms of the personal pronouns. Transitive verbs and prep- 
ositions are said to "govern the objective case" of these 
words. But nothing in the form of a noun object of verbs 
and prepositions reveals that it is in the objective case ; that 
property must be learned by determining in what relation 
it stands to the so called "governing" word. In this term 
govern we have an appropriation from the grammars of 
those languages that are really inflected. In Richard Grant 
White's "Words and their Uses," he vigorously insists upon 
the extreme absurdity of many of the "rules" of syntax, and 
'^ specially upon the "ridiculous use" we make of the word 



82 



PEDAGOGICS OF GRAMMAR. 



govermncnt. He says, "No term was ever more unwisely 
chosen than governinoit to express the relations of words 
in sentences. ... In grammar it implies, or seems to 
imply, a power in one word over another. Now, there is in 
no language any such power, or any relation which is properly 
symbolized by such a power " ; and much more in this strain. 
It is a subject for the student's consideration, who must, 
however, remember that many eminent authorities are at 
variance with Mr. White and with one another with respect 
to this matter. Certainly, a great deal of useless and con- 
fusing verbiage has been introduced into the treatment of 
English grammar. 

95. JA^t of Prepositions. — The student has already 
been apprised of the adverbial origin of prepositions. But 
when adverbs became prepositions, they kept their adverbial 
character, so that nearly all of them may still be used as 
adverbs. To employ them as adverbs, we merely omit their 
object noun or pronoun. The following is a list of the prin- 
cipal prepositions: 



aboard, 


betwixt, 




past, 


about, 


be3'ond. 




pending, 


above, 


by, 




regarding, 


across. 


concerning, 


respecting. 


after. 


down. 




round, 


against, 


during, 




since, 


along. 


ere, 




tell, 


amid. 


except, 




through. 


amidst. 


excepting, 


throughout. 


among. 


for. 




to. 


amongst, 


from. 




touching. 


around, 


in. 




toward. 


at. 


into. 




towards, 


athwart, 


mid, 




under, 


bating. 


midst, 




underneath. 


before. 


notwithi 


standing, 


until, 


behind, 


of. 




unto, 


below. 


off, 




tip, 


beneath, 


on, 




upon, 


beside. 


out, 




with, 


besides. 


over, 




within, 


between, 


overthw 


art, 


without. 



§ 4 PEDAGOGICS OF GRAMMAR. 83 

96. Use of Prepositions With. Certain "Words. — 

Much care is required in the use of prepositions with some 
other words. Of these words there are so many that only a 
partial list can be given. The choice is generally deter- 
mined by the meaning of the prefix of the word associated 
with the preposition, but often by the meaning of the entire 
word. 

Absolve f7-om a promise. 

Abstract of a legal document. (An outline of its contents.) 
Abstract /Vtfw, as cash from a drawer. 
Abhorrenceyi^r a person or thing that one hates intensely. 
Abhorrence of something we dread ; as, snakes, spiders. 
A choice hetiveen two, or among many. 
Accord loith a view or an opinion of another person. 
Accord in an opinion held by two or more other persons. 
Accord to some one a privilege or a right. 
Accomplish by diligence. (As a means.) 
Accomplish with difficulty. (Any object striven for.) 
Accomplish tinder hard conditions or terms. 
Acquit of a. charge, i^otfrom, as formerly.) 
Acquire by labor. 
Affinity between friends, ideas. 
Adapted to, fitted or adjusted to intentionally. 

Adapted /<^;- grazing, _/<;;' ioo^, for supporting life. (Natural suit- 
ability for.) 

Agree with a person. 

Agree to an arrangement or a stipulation. 

Changeyiyr, a wagon /"i;;r a horse. 

Change with, seats with some one at a theater. 

Change in voice, behavior. 

Change <?/" circumstances. 

Confide /// the honesty of some person. 

Confide to a person the care of a child. 

Confident of her charm. 

Confident in the correctness of his position. 

Conference between two persons or parties. 

Conference about, regarding, or concerning a matter. 

Confer on or upon a person any favor. 

Confer with a person or party, or about any matter. 

Confirm in a suspicion or a belief. 

Confirm by argument or evidence. 

Comply with regulations. 

Convenient to the station. (A place.) 

Convenient/^;;- any purpose ; as a \>oo\ifor reference. 



84 PEDAGOGICS OF GRAMMAR. § 4 

Correspond with a person and to a thing. 
Dependent on or upon a person's word or promise. 
Dependent 0/ a king or 0/ any person or thing that supports. 
Differ 7L'/t/i a person, or from an opinion or a statement. 
Different in some respects, or from what was thought or expected. 
Dissenty>(?;;z an opinion or a statement. 

Die <?/" fever (disease), by violence, y^ir the country, to the world. 
Exception yrf/w a rule, or to some remark or statement. 
Fall tinder suspicion ; into error or difficulty. 
Influence by, or by means of, some power from without. 
Influence through, by, or by means of some quality within. 
Insist upon going, or upon some claim, or matter in dispute. 
Involved in trouble ; with some one. 
Need of money ; for or of help, advice, assistance. 
Offensive to a person, iti manner or in some quality. 
Part from a friend ; with a thing. 

Reconcile to one's lot or to a person; something with a statement or 
an event. 

Share in the transaction ; of the profits. 

Taste of iood or drink; for mathematics, music. 

Thirst for or after knowledge. 

The foregoing is only a mere fraction of the words that 
involve uncertainty in the use of prepositions. It is only by 
constantly consulting standard authorities that the student 
can become expert in this matter. 

97. Misuse of Certain Prepositions. — Ambiguity is 
very frequently caused by the careless use of prepositions. 
To illustrate, one would not believe that the little word.^y 
could give much trouble, but no preposition is so often mis- 
used. When, for example, it connects two words, one 
denoting an agency that may produce a result denoted by 
the other word, the meaning is nearly always ambiguous. 
Thus, 

" The peace of God" may mean the peace that He enjoys or that He 
confers. 

"The story oi Ben-Hur" may denote the story told about him or 
by him. 

"The choice oi Hercules." Does it mean that he chose something, 
or that he luas chosen ? 

"The ivelcome of JMacleod," "The defiance of Catatine," "The 
doubt of Hume." 



§ 4 PEDAGOGICS OF GRAMMAR. 85 

The student will at once notice the ambiguity of such 
expressions. Nor does it improve matters to substitute 
the possessive case: "God's peace," " Ben-Hur's story," 
" Macleod's welcome," etc. The only remedy is tore-cast 
the expressions: "The story told concerning Ben-Hur," 
" Cataline's defiance to the Senate," "The doubt enter- 
tained by Hume," " Macleod's welcome to his clansmen." 

Many other prepositions are misused, among them on and 
iipoii^ among iind bcizvccii, by and zoit/i. 



TABIiE OF THE PREPOSITION. 

r Time. — at night, by noon, after midnight. 

Place. — in the army, into the house, upon the mountain. 

Agency. — by force, zvith a gun, he succeeded through me. 
CLASSES \ Reason.— for his health, at my request. 

Possession. — the wife of vaj friend, a ship ^y^ France. 

Exclusion. — ivithout mercy, against my wishes, 
i Materia I. — of gold . 

Many other clas.ses of prepositions are given, but no 
classification includes them all. 



THE co:n^ju?^ction. 

98. Coiineetlves. — We have seen that any word placed 
between two other words with such reference to their mean- 
ing as to bring them into relation is, in so far as it does this, 
a connective. Such conjunctive or connecting value is usually 
accompanied by some other and more conspicuous function 
that determines the part of speech to which a word so used 
belongs. Thus, the earth is round, words that burn, written 
by Burns, died ivliere he fell. Jack and Gill. The italicized 
words are all connective in fimction, but, except the last, 
each has some other office. 

The verb is not only connects eartJi and round, but placed 
between them, it has assertive or predicating value. By its 
use the words are combined into a statement. 



86 PEDAGOGICS OF GRAMMAR. § 4 

The relative pronoun, besides being a connective, repre- 
sents and relates to an antecedent nou)i ox pronoun, and is, 
for that reason, called a relative pronoun rather than a con- 
junction. 

Again, the conju)ictivc adverb is a connective that modifies, 
as the ordinary adverb does, each . function being about 
equally prominent; its double office gives it its name. 

1^\\.Q preposition belongs among the connectives also, but it 
is named from the fact that it generally stands before a noun 
or a pronoun With this noun or pronoun it forms a phrase 
either adjective or adverbial. The fact of its pre-position is 
hardly a sufficient basis for its name, but this name was 
chosen and generally accepted long ago, and must for that 
reason be retained; besides, it would perhaps be impossible 
to find a better. Relation zoord has been suggested, but, as 
we have seen, nearly all words are more or less relational. 

Another word used primarily as a connective of clauses is 
the conjunction. When it is employed to join clauses of equal 
rank — coordinate clauses — its office is almost entirely connect- 
ive. It is the plus sign of language. The conjunction so used 
is named from the equal or coordinate rank of the connected 
elements. These words, which connect clauses of equal 
grammatical rank, of which there are not many, and of which 
and is the best type, are called coordinate conjunctions. 

99. Coordinate or Coordinating Conjunctions. — 

These conjunctions have been divided variously, but the 
following is perhaps the best classification: 

1. Copui.ATivK — consisting of and, which unites and 
nothing more, and some that are equivalent to and with some 
added adverbial effect. These are such as also, likezvisc, too, 
besides, noiv, moreover, well, so, then, etc. 

2. Alternative — conjunctions that imply a choice or a 
rejection of alternatives; as, or, nor, either, neither, else, 
cither — or, ncitlicr — nor. 

3. Adversative — ^conjunctions connecting elements that 
imply something adverse or in opposition ; as, but, yet, still, 
save, except, nevertheless, provided, although, however, etc. 



§ 4 PEDAGOGICS OF GRAMMAR. 87 

4. Illative — conjunctions used in reasoning to denote 
inference, conclusion, consequence; as, tlwrcforc, hence, 
ivJiciicc, tlins, consequently, etc. 

100. Subordinate or Subordinating Conjunctions. 

When the connected elements are of unequal rank, the con- 
junctions used to connect them are called subordinate ox sub- 
ordinating conjunctions. 

Besides connecting-, these conjunctions take on the adver- 
bial function, in some cases so strongly that it is impossible 
to separate them from the conjunctive adverbs. Some of 
them are if, since, before, unless, after, except, for, although, 
unless, that, etc. 

To its simple connective force the subordinate conjunction 
may add the adverbial designation of : 

1. Plack. — " He was killed where the monument now stands." 

2. Time. — " He was arrested as he was leaving the city." 

3. Cause. — " The king was killed because he was a tyrant." 

4. Purpose. — ^" The man toiled that he might educate his children." 

5. Comparison. — " Henry is more diligent than his brothers are." 

101. Corresponsive or Correlative Conjunctions. — 

Conjunctions become correlative when used in pairs. The 
principal of these are />^V/;-(^?//^/, as-as, as-so, if-then, eithcr-or, 
neither-nor, whether-or, thongh-yet. 

103. Tlie Adverbial Elements in Conjunctions. — 

The only difficulty of any account with the connectives of 
various kinds is in classifying them so that they may be kept 
separate. But this is really of little consequence. There is 
no impropriety in calling a subordinate conjunction having a 
decided adverbial quality a conjunctive adverb. The truth is 
that no one ever has succeeded in drawing a definite line of 
division between conjunctions and adverbs, and no one may 
hope to do so. Nearly all conjunctions w^ere originally 
adverbs, and have, in most cases, manifested a tendency to 
return when their services are required. 

Moreover, many subordinate conjunctions and some con- 
junctive adverbs may be used as prepositions. The student 
will find no difficulty in verifying this statement. 



PEDAGOGICS OF GRAMMAR. § 4 



tabijE of the conjunction. 



1. Coordinate 



CLASSES \ 



\^ 2. Sitbo7'dinate 



{ Copulative. — and, also, likewise. 
I Alternative. — or, nor, either. 

Adversative. — but, yet, still. 

Illative. — consequently, therefore. 

Place. — where, whence. 

Time. — when, as, until, since. 

Cause. — why, wherefore, because. 
I Purpose. — that, so that, in order that. 
(^ Comparison. — than, so-as. 



THE INTERJECTION. 

103. Interjections Not a Part of Speech. — It has 

already been said, in substance, that the interjection comes 
to us from the time of the earliest history of the race. It is 
found in all languages, and is a sign more of the inability to 
express thought than otherwise. Its use characterizes the 
first efforts of children to convey their thought to those about 
them. Strong feeling of any kind — hatred, fear, bodily sen- 
sation, earnest desire — leads to the selection of a word signifi- 
cant of such feeling. This word stands for the words that 
cultivated people employ to express thought in completeness. 
Thus, most interjections denote more or less exactly the 
feeling of the speaker. Any part of speech, therefore, may 
represent a thought, in the entire expression of which the 
word would often be conspicuous. Hence, we have such 
interjections as hush! mum! adieu! shame! soft! behold! 
welcome ! 

104. Interjections Generally Echo the Sense. — 

There is a figure of rhetoric called onomatopccia applied to 
words that by their sound more or less clearly indicate their 
meaning. Such are the sounds made by animals or by some 
of the forces of nature; as, buzz, bang, baa, crash, hist, soft, 
roar, hum, etc. 

If the student will carefully examine the list of interjec- 
tions commonly given, he will find that they have in large 



§ 4 PEDAGOGICS OF GRAMMAR. 89 

measure this quality. Thus, the interjeetions most used to hail 
some one at a distance contain the long sound of o^ and this 
sound is prolonged at pleasure. Those that enjoin silence 
and caution contain the sound of jt and the short sound of i. 
To denote doubt, contempt, incredulity, the long sound of e 
is frequent, and this is the sound that is prolonged ; as, 
indeed! really! ' 

Most interjections, therefore, have vowel and consonant 
combinations that can be prolonged at pleasure, or that echo 
the sense by the sound. One eminent authority calls attention 
to the fact that "■ all languages contain as an interjection the 
long sound of c^" In general, the open long vowels are 
employed in interjections intended to express emotion 
strongly and without concealment; the short vowels and the 
liquid or hissing consonants are used when the emotion is to 
be restrained. 

Strictly, very many interjections have no meaning other 
than that denoted by the tones and gestures characterizing 
their utterance. Thus, ah! oil! may be used to express a 
great variety of sentiments and emotions, but these must be 
gathered from the circumstances attending their use, from 
the inflections and intonations employed in pronoimcing 
them, and from many other things. 

This .subject, while curious and interesting, is not one that 
need long detain the ordinary student. 

105. Division of Interjectious Into Classes. — These 
words have been arranged under various heads ; as, of joy, 
wonder, sorrow, praise, surprise, disapproval, pain, fear, 
calling, etc. But to prepare such a list as the various author- 
ities would regard complete would be impossible, since many 
words, considered by some as interjections, are by others 
classed differently. Such, for example, as avaniit ! hist ! 
hark f bcJioId ! are only verbs in the imperative mode, and 
good! excellent! sad! etc. are adjectives. 



PEDAGOGICS OF GEOGRAPHY. 



IXTT^ODucTIo:^^. 



EDUCATIOXAT^ VALUES. 

1. Of Value in General. — Much has been said and 
written about educational values. The various theories on 
the subject, although they are not vitally necessary to the 
science and art of education, are yet of so much importance 
that a modern and prog-ressive teacher should give careful 
attention to the matter. 

Before proceeding to consider the subject of the various 
values of the subjects tavight in the schools, it is necessary to 
inquire what the term value means. The word comes into 
our language from the Latin. The verb ^^^/rr^' means "to 
be strong or robust " — to have vigor or efficiency. Like 
nearly all words from the ancient languages, its original 
application was to things physical and sensible — to the 
objects and concerns of cominon life. In process of time, 
its use was extended to the domain of thought and reflec- 
tion — from the concrete and material to the abstract and 
ideal. But in its transfer, the underlying trope or metaphor 
is retained, and the notion of mere physical strength has 
been made to include other potencies than those of matter. 
So the term value is now used with reference to anything 
that may become an agent or factor in accomplishing a 
result of any kind — in attaining something that directly or 

§5 



2 PEDAGOGICS OF GEOGRAPHY. § 5 

indirectly contributes to the satisfying- of desire or need. 
Anything helpful as a means to an end has, by virtue of 
that helpfulness, value with respect to that end. On the 
other hand, whatever has no such efficacy is without value — 
worthless. The air, the rain, the sunlight, and the multi- 
form forces of nature are agencies of value; so also are 
reading, conversation, study, reflection, investigation, rea- 
soning, patriotism. 

J^aluc, then, is the desirability or worth of a tiling, on 
account of its cffi.cicncy, real or imagined, in securing some- 
thing desired, or in avoiding the opposite. 

3. Value Is Relative, ^NTot Absolute. — Nothing is more 
difficult to fix than a uniform standard of value. To secure 
an invariable standard of weights and measures, the French 
measured, at great expense and with extreme care, the dis- 
tance from Barcelona to Dunkirk, and from the result they 
calculated the length of a meridian from the equator to the 
pole. This quadrant they divided into ten million equal 
parts and called one of the parts a meter, which they took as 
a national standard of length. They made of platinum- 
iridium a rod representing the exact length of a meter, and 
sent duplicates of it to each other nation, in the expectation 
of making it a world standard. But the element of human 
error could not be excluded, for it was afterwards foimd that 
the quadrant of the earth had not been measured correctly. 
Even if it had been, the length of the metal rod would 
change with every variation of temperature. 

The only other standard of physical length is a pendulum 
that oscillates in one second in the latitude of Greenwich, 
England. Such a pendulum is a standard yard, and its 
length determines the weights and measures used in coun- 
tries where English is spoken. But the lengths of the yard 
and the meter are alike variable and uncertain. There can 
be no such thing in the physical world as an absolutely 
invariable standard of any kind. The same is true in the 
ideal world — the domain of immaterial utilities. All values 
of every kind are relative. Those having reference to human 



§ 5 PEDAGOGICS OF GEOGRAPHY. 3 

needs, both physical and ideal, vary iniceasingly. They are 
affected not only by temperature, but by temperament, by 
the changeable human measurement of fact and fancy, by 
the shifting relations among things, and by innumerable 
other circumstances and uncertainties. A cannon ball has 
no inherent and constant capacity for destruction. The value 
of gold is conventional, a matter of agreement merely. 
Circumstances may arise in which it will be valued no more 
highly than iron. The coins found by Robinson Crusoe 
were worthless to him, and it was a matter of indifference to 
him whether they were gold or silver. In either case, they 
had for him no value as a means to an end — they could not 
be instrumental in satisfying any of his numerous wants. 
The value of a bushel of wheat is neither intrinsic nor con- 
stant; it changes with demand and supply, and with the use 
that is made of it. A great sculptor would be less effective 
and useful as a quarryman than one trained for the work ; 
the designer of a battle ship or of a great bridge would find 
his situation in the wilds of Africa more beset w^ith dangers 
and difficulties than if he were a native savage. A treatise 
on cuneiform inscriptions or Egyptian hieroglyphics could 
have no interest or value to an unlearned man, nor would a 
work on calculus avail anything in the training (jf a child. 

In the last analysis, all value is relative to human needs, 
and these are constantly fluctuating, in consequence of 
changing conditions. Now, hmnan needs are mainly of two 
kinds, physical and mental, and they vary for different indi- 
viduals, and change with time and place. Hence, for train- 
ing the mind and perfecting the physical faculties, the best 
methods and appliances in one case are by no means so in 
every other. The ideal education of a boy would be entirely 
tnisuited, or nearly so, for his sister; and the method to be 
pursued with a bright boy would not be equally good with a 
dull boy. It is the old story — what is one man's meat is 
another man's poison. Value, as well as nearly everything 
else, is relative and changeable. 

It follows, therefore, that educational values cannot be 
fixed and durable. 



4 PEDAGOGICS OF GEOGRAPHY. § 5 

3. The "^Ne^v^" Education. — In view of the fluctua- 
tion and uncertainty in value of every item included in our 
courses of study, it is important that the student should con- 
sider just what should be understood by the expression, 
'' The New Education." We are hearing it often, and under 
circumstances implying that there is an old education, with 
old methods and old subjects of study making up its curric- 
ulum. Now, the student should remember that the world 
furnishes very few examples of sudden and radical change. 
It is indeed true that " old things pass away, and all things 
become new"; but this happens not suddenly, but gradually. 
The history of the introduction of the new is that it is at 
first sneered at and ridiculed, then argued, with gradually 
decreasing bitterness, and finally accepted, often after many 
years. When matches were first offered for general use, our 
rural grandfathers objected to them for a long time because 
of the ease with which their barns could be burned. This is 
an illustration of the first estimate placed on things that finally 
come to be regarded as indispensable. In the days before 
railroads and steamboats the horizon of each individual shut 
in for him the world. A man saw the sun rise at one edge 
of creation and set at the other. The most capable and 
scholarly teachers knew nothing of geography. Most of them 
had never heard the word, which even to pronounce was 
sufficient evidence of profound and unusual scholarship. No 
enterprising publishers competed in supplying textbooks on 
the subject. Indeed, they were beyond the printer's art in 
this country, as much as they were beyond the power of pur- 
chase by the average parent. The same is true of every 
subject of study, with the exception of the "three R's," 
reading, writing, and arithmetic. Of arithmetic, even, it 
was not considered important that girls should study it. 
They would have no use for it; and utility then, as now, was 
the criterion of value. Each of the many subjects that now 
overcrowd the courses of study has made a place for itself 
only after a long struggle through a period of growing need 
for it. 

In this gradual way the old passes away after a long period 



§ 5 PEDAGOGICS OF GEOGRAPHY. 5 

of diminishing usefulness. Nothing in human progress, if it 
is really useful, can be or should be sudden. 

So that, when the advocates of the supposed new educa- 
tion cry down the old and cry up the new, when the patient, 
plodding teacher, trying to make the best out of existing 
conditions, is denounced as an old fogy, and his matter and 
method are said to be antiquated, he should remember that 
there is no more a new education than there is an old one. 
What he is doing and his way of doing it are very probably 
a little behind the requirements of his immediate surround- 
ings; but this is in consequence of an unavoidable inertia that 
belongs with general progress and partakes of the character 
of a cautious conservatism. The tides are always behind the 
direct line of the moon's attraction, and the highest tempera- 
ture of day is not at noon, but a couple of hours later. Be 
very sure that these things are true: that no one can be 
found whose training exemplifies a " new education "; that 
no one can tell you where a teacher that practices it can be 
found ; that no one can prepare a course of study in accord- 
ance with it; that there is not, never will be, and never 
ought to be such a thing as a new education. It is only the 
watchword of the educational charlatan. Every profession 
has its humbug, and this perhaps will always be the case; for 
the average man seems not to be quite happy unless he is 
regularly imposed upon; he is an easy victim to the alluring 
advertisements of "yellow" journalism. 

Lest a wrong impression be left, and that the writer be 
accused of opposing educational improvement, it is necessary 
to state here that every true teacher is an advocate of growth 
and progress. The ambitious and intelligent teacher must 
keep himself informed with respect to this inevitable and 
necessary growth in educational method and matter. He 
must not be deceived and led away after the ' ' strange gods " 
of the professional reformer. He must remember that, 
before he lets go the old, he should have good reason to 
know that what is offered as a substitute is better. If, 
however, he allows himself to get too far ahead of the natural 
and orderlv march of the general mass, his power as a worker 



6 PEDAGOGICS OF GEOGRAPHY. § 5 

will be nearly destroyed by the opposition he must meet. 
His usefulness will in that case be no greater than that of 
the teacher too far behind his time. Let the teacher aim to 
be neither a radical nor a conservative, but to temper the 
restless yearning of the one for better things with the cau- 
tious wisdom and persistent plodding of the other, '■^ Prove 
all things; holdfast that which is good/' 

4. Diversity of Oijiiiiou Concerning Educational 
Values. — In an address on "What Knowledge Is of Most 
Worth > " delivered at a recent annual meeting of the 
National Educational Association, by its president, that 
official, after dwelling on the many unsatisfactory and widely 
divergent answers that have been made to his query, pro- 
ceeds to formulate a response as follows: 

If it be true that spirit and reason rule the universe, then the highest 
and most enduring knowledge is of the things of the spirit. That sub- 
tle sense of the beautiful and the sublime which accompanies spiritual 
insight, and is part of it, is the highest achievement of which humanity 
is capable. . . . To develop this sense in education is the task of art 
and literature, to interpret it is the work of philosophy, and to nourish 
it the function of religion. Because it most fully represents the 
higher nature of man, it is man's highest possession, and those studies 
that directly appeal to it and instruct it are beyond compare the most 
valuable. 

Most writers on education are guilty of the fault of dealing 
in poetical and meaningless generalities, that, while very 
pretty and melodious, are yet vague and of no possible use 
to the seeker after practical guidance and available help. 
These flights into the empyrean are, no doubt, very stimu- 
lating to the "higher nattire " and the "spiritual insight," 
but they take us nowhere; they fail to furnish any light or 
help on the practical questions involved in the education of 
our children. And this light and help are exactly what the 
teacher wants. He that would wisely and helpfully prescribe 
the zahat and the hoza in education must forget somewhat 
the "infinite possibilities of the human soul," " the subtle 
sense of the beautiful and the sublime," and must remember 
temporal wants and actual conditions. The thing that man 



§ 5 PEDAGOGICvS OF GEOGRAPHY. 7 

is most in need of just now is assuredly not "spiritual 
insight," "soul culture," "sweetness and light, " or "ears 
attuned to the higher harmonies," whatever these are; his 
most pressing necessities are of the earth earthy. He must 
earn bread for himself and for those dependent on him, he 
must become an expert and efficient agency in modifying his 
surroundings and turning them to practical account, he miist 
equip himself with mental and manual aptitudes that have a 
market value, he must gain " the wrestling thews that throw 
the world. " This seems like a humiliating descent from the 
serene heights whence " spirit and reason rule the universe. " 
But this is one of the conditions imposed on us by the fact 
that we live in a world where most of us eat bread that must 
be earned at the expense of the tis.sue of brain and muscle. 
Our boys and girls cannot breathe the thin air of those spirit- 
ual altitudes, and we have learned the hard necessity of 
moderating our hopes and dreams about the future of our 
children to the simple wish that we may be able to prepare 
them to meet with fair success the requirements of the life 
that awaits them. 

The writer does not wish to be understood as insisting 
that life has no place for those finer feelings, those vague, 
intangible yearnings and hopes and dreams, those soul har- 
monies and fancies fine, about which we hear so much and 
really know so little. He insists merely that whoever fails 
to prepare to do efficiently the practical work that awaits 
him will make a pitiful failure of the business of living, 
however thoroughly trained he may be in the transcen- 
dental culture that is alleged to rule the universe. He that 
acquits himself up to the fullest measure of his capacity in 
the duties of practical life is perhaps making the best possi- 
ble preparation for the conjectural future. 

Inasmuch, then, as there are so many and such diverse 
views of values in education, it is important that the teacher 
should have some standard or criterion by which he may 
judge for himself the usefulness of the many things that are 
urged upon him. And this .seems the best and safest — to 
consider carefully in zv/iat loay and to what extent any subject 



8 PEDAGOGICS OF GEOGRAPHY. § 5 

or method zvill have real praetieal value in the fiittire life 
work of his pupils. How and in what measure will arithme- 
tic help, or geography or drawing or languages or philoso- 
phy ? You should ask yourself, "Is this new method, or 
this recent theory better, more helpful,- more in consonance 
with reason and experience than the method or theory I am 
now following ? " Insist upon definite reasons for changing 
your plans before you change them. Your pupils are about 
to enter a life that is full of importunate realities and impera- 
tives that cannot be ignored, and your responsibility for 
properly preparing them for it is great. 

5. Educational Values As Affected by Existing 
Conditions. — The values of the various subjects included 
in courses of study are much ailected by circumstances of 
time and place. What is indispensable in a certain place at 
a given time does not remain so for all times and places. 
And, as has been already remarked, that which is best for 
one child or set of children is otherwise for children differ- 
ently situated. These difficulties become apparent in the 
attempt to educate children in masses, without regard to 
home conditions, sex, future employment, and differing 
degrees of intelligence. It becomes necessary to devise the 
best possible average course of study. That it should be an 
average curriculum comes from the obvious fact that no 
scheme of education for a large number of children together 
can provide for their individual wants, or give a discrimina- 
ting treatment to each child. The physician may do this — 
must do this — with his patients, but it is impossible with the 
teacher. The boy and the girl, the dull pupil and the bright 
one, the child from the home of refinement and the child from 
the home of ignorance and squalor, are all on equal terms 
with respect to education in the public schools. And yet an 
ideal training requires the same special treatment of individ- 
uals that the phj^sician gives his patients. One pupil should 
receive much mathematics and little science, while these 
conditions should be reversed in another case. 

Because their activities in the future are to be unlike, the 



§ 5 PEDAGOGICS OF GEOGRAPHY. 9 

needs of our boys differ from those of our girls. As 
compared with the boy, the girl needs little mathematics 
and less science, and yet it is impossible to separate the sexes 
during the primary education beyond which so few go. 
As density of population increases, the division of labor will 
doubtless be gradually introduced into the work of teaching 
and these difficulties will be lessened or removed altogether. 
The graded schools of our cities and large towns, with their 
partial specialization of the teacher's work, furnish a hint of 
better things to come. 

If education is only adaptation, — the fitting of powers for 
work to be done, — then the various powers must be trained 
with constant reference to the work that awaits them. A 
perfect locomotive engine would have no value whatever 
for driving an ocean steamer. Even if it were possible to 
foresee in every case in what exact line of life's activities 
each of our children is to find his future work, it would 
clearly be impossible, without great expenditure of thought 
and money, to educate each for his destined career. No one 
has the needed foresight. Obviously, then, the question of 
education resolves itself into one of average adjustment. 
From the almost limitless field of human knowledge must 
be selected those studies that will probably furnish the 
student with the best average preparation for life and its 
duties. Under existing conditions, this is the best that can 
be done. 

6. Primary and Secondary Education Should Be 
Parts of One Sclienie. — Another circumstance that has a 
bearing on educational values is the necessity for continuity 
of plan from the beginning to the end of educational work. 
Most of our children leave school at the close of the elemen- 
tary school course, or even before it is finished. On the other 
hand, many children continue into or through a secondary 
course — the academy and high school — and then enter the 
college and the professional school. To prevent a break 
involving much loss of time between the primary and the 
secondary schools, the former should, as far as possible, be 



10 PEDAGOGICS OF GEOGRAPHY. § 5 

preparatory for the latter, and the latter should be equally 
well suited as a preparation for college. In other words, 
our public schools should have in contemplation the fitting 
of its pupils both for life and for college. This neces.sity, 
together with the difficulties arising from individual differ- 
ences, mental, physical, and sexual, added to the varying 
requirements and imcertainties of life's activities, renders 
this subject one of the most involved that can confront the 
educator. This fact is shown in the constantly recurring 
questions of parents: " How shall I educate my son? 
What are his natural aptitudes? What can he be trained 
to do better than he can do anything else?" "And my 
daughter — what is best for her? " To these important ques- 
tions each school and each educator has a different answer. 
One recommends science, another indiistrial training; one 
commends the classics, or "spiritual insight," and still 
another tells of the " all-conquering power of thought." In 
the end, nothing is definitely settled except that our children 
must do as their parents did — avail themselves of such 
opportunities of training as they may chance to meet. 

7. General Classifleation of Studies. — In an able and 
thoughtful paper on "Educational Values," our present 
Commissioner of Education, Dr. William T. Harris, gives a 
general outline of the subjects in which a man should be 
educated from first to last, and a logical statement or view 
of the phases of his nature that are properly related or 
adapted to each subject or group of subjects. His aim is to 
present a scheme of education that shall train tJie ivhole man 
in all the range of his powers, and that shall have unity and 
cohesion from the lowest primary to the finishing work of 
the college and the technical or professional school. Such a 
scheme will give to the course, if broken at any point, a 
degree of harmony and completeness much to be desired. 
Of course his plan does not, and cannot, take into account 
differences among students and their surroundings. P^. 
Harris considers man as being simply an inhabi'^'^rt o' 
world, in which he is to play his brief part. Of man's 



§ 5 PEDAGOGICS OF GEOGRAPHY. 11 

relation to a sphere wider than the earth he takes no account. 
Training for that sphere he leaves to the care of religion. 
Considering man apart and in himself, and afterwards in 
relation to immediate surroundings, Dr, Harris proceeds to 
classify the various subjects of study with respect to the 
powers that they are instrumental in training. His purpose 
is simply one of adjustment. 
He says: 

The theory of man includes three phases: 

1. Man as a practical being, a will power, a moral being acting 
socially and politically — a history maker. 

2. Man as a theoretical being, a thinking power, a rational being 
giving an account to itself of the world and itself — a science maker. 

3. Man as an artist, a being that represents or portrays himself, 
embodies his ideal in real forms, makes the visible world into his own 
image — a producer of art and literature. 

The foregoing are the phases of himself that man presents 
to be educated. For the cultivation of the whole man the 
range of studies covers the domain of nature and that of 
j/ian, or spirit. 

f ^ ^ ( Mathematics. 

I. Inorganic. — ■ . . , -,. ^, 

IN'atiire. - ' Jrhysics, including Chemistry. 

[^ II. Organic. — Natural History in its widest sense. 

f III. Theoretical ok Thinking Power. — Logic, Phi- 
losophy, Linguistics. 
Man, or I 
Siiirit ' ■ Pi^'^ctical or Will Power. — Civil History, Social 



and Political Sciences. 
V. Esthetic or Art Power. — Literature and Art. 



Answering in the elementary schools to these five general 
groups, we have the following: 

I. Xatiii'e Inorganic. — Arithmetic, the mastery of 
number. 

II. Nature Orj^aiiio. — GcograpJty, the mastery of 
place. 

III. 3Iaii Tlieoi'ctical. — Graiiimar, the mastery of 
letters. 

IV. Man Practical. — History, the mastery over time. 
V. Mail Estlietic. — Reodiiiir and Literature. 



12 PEDAGOGICS OF GEOGRAPHY. § 5 

The studies given above for these five subdivisions of 
culture are those that should be found in the curriculum of 
the elementary schools. In the high school and academy 
each subject is extended. 

Arithmetic is continued, but to it are added, in the 
domain of mathematics, algebra, geometry and trigonojn- 
etry, analytical geometry, natural philosophy, and chem- 
istry. 

Geograpliy, belonging under the division of organic 
nature, takes on physical geography, astronomy, botany, 
physiology, and zoology. 

Graminar, the science evolved by man as a thinking 
power, and most useful in developing in him the power of 
abstract thought, is extended into the domains oi philology, 
ancient and modern languages, linguistics in general, and 
mental and moral science. 

Civil History, a science that owes its existence to man, 
considered as a will power working in national masses, 
becomes, in the secondary schools, universal and comparative 
history, civics, and the constitution of the student's own state 
and country. And, finally, 

Heading- and Tjiterature, the studies appropriate to 
esthetic man, include the history of tJie literature of his 
language, the study of its best typical examples, rhetoric and 
drazi'ing, with other suitable art work. 

In the college and the professional and technical schools, 
the field is still further widened, with special emphasis along 
lines directly concerned in particular professions. 

8. Completeness of tlie Foreg'oinjif Classification. 

With the exception of the spiritual side of man's nature — a 
part of him that is believed to share in another existence 
beyond the present — provision is made in the scheme indi- 
cated above for his ciilture in every aspect of his being. His 
religious or spiritual training is left to be the care of the 
church. No attention is given to the perfecting and main- 
taining of his mere physical powers, but none is required. 
The necessary and usual employment of those powers is 



§ 5 PEDAGOGICS OF GEOGRAPHY. 13 

generally sufficient to preserve their vigor; if more is for 
any reason needed, it is easily found. 

The zvorld, in every aspect in which it stands related to 
man, is made a matter of special concern and systematic 
study; man himself, regarded both as a power operating on 
nature for his own support and advantage, and as a being 
capable of improvement and happiness, is to be thoroughly 
and symmetrically trained. The development and culture 
contemplated are all-sided, and every subject included is 
indispensable to an ideally complete education. 

It is evident, therefore, that it is a narrow and incomplete 
view of education that prompts men to go about with the 
various and conflicting cries: "Know thyself"; "Study 
science, for science is all in all"; "Seek after spiritual 
insight, for spirit and reason rule the universe"; "Mathe- 
matics is the skeleton of God's plan of the universe; there- 
fore, study mathematics." The adjuration should be rather: 
"Know thyself and nature also; study science, and seek 
after spiritual insight; but with all thy seeking, neglect not 
matliematics. " 

The student must remember, however, that a scheme of 
education like this, or any other that may be proposed, can- 
not be realized in completeness. Our limitations of every 
kind are too many; circumstances constantly interfere with 
our plans, and compel us to change or abandon them. The 
merit of this plan of education is, that, if at any point it is 
interrupted, the zvork is all-sided, Jiarnionious, and complete 
7ip to that point. However far man's education may be car- 
ried, it is never finished, since he is capable of indefinite 
advancement. 

9. Specialization in Education. — vSomewhere in the 
course of the general training indicated above, special prep- 
aration for some particular activity in life must begin. If 
one wishes to become a lawyer, a physician, an engineer, or 
a teacher, he must take up, at the close of his college course, 
those studies the mastery of which will make him proficient 
in his chosen profession. He cannot expect to become 



14 PEDAGOGICS OF GEOGRAPHY. § 5 

expert as a specialist by mastering a general curriculum 
alone. Hence, it is easily apparent that, if he is to become 
a physician, for example, there are certain lines in the 
general-culture course that for him should be emphasized 
and amplified. Those subjects that should be dwelt on and 
made prominent are different for each different profession. 
The engineer finds indispensable a thorough mastery of the 
laws, properties, and forces of inorganic nature ; the physi- 
cian should be most familiar with organic nature, in both its 
animal and its vegetable structures, while of almost equal 
importance are certain lines of inorganic nature; the clergy- 
man should be expert in the sciences pertaining to man 
regarded from the theoretical, practical, and esthetic stand- 
points — in the third, fourth, and fifth divisions of Dr. Harris's 
general scheme. 

It appears, then, that specialization in education is neces- 
sary if we would attain to the greatest possible efficiency in 
particular directions. It is equally evident that the earlier 
this preparation for some selected life work is begun, the 
more thorough it will be ; but it must be remembered that 
every gain in this respect will entail a corresponding loss in 
the general broad culture that we have outlined. It is an 
important question, therefore, whether the gain on the one 
hand compensates for the loss on the other. Evidently 
there is a golden mean to be sought in this matter as in 
nearly every other. How often we meet professional men 
that seem to know little beyond their immediate profession; 
and is there not in such cases a strong suspicion aroused that 
the specialist is really an incompetent ? Does this physician 
that knows physic alone really and broadly know even that ? 

So that those subjects that have special educational value, 
from the fact that they are indispensable to some profession, 
lose in value when overattention to them leads to the 
neglect of some other subject necessary as a preparation 
for them. For example, it is loss in thoroughness for a 
pharmacist to give so much attention to the study of the 
phannacopoeia that he fails to learn chemistry and botany. 
Thus, these two related necessities in preparing for life — ■ 



§ 5 PEDAGOGICS OF GEOGRAPHY. 15 

general culture and professional training" — complicate the 
question of educational values. As before stated, value is 
relative and not absolute. Any subject needed in special 
training' rises in value in proportion to the broadness and 
thoroughness of culture in him that pursues it. The con- 
trary of this is true. There should, then, be a wise super- 
vision in education, to preserve a just balance between 
study for general culture and that for special training, in 
order that the former may not be continued too long or 
extended too widely, and that the latter may not be begun 
too late or have a range too narrow. 

10. The Liiberal and tlio JLiiicrative Sciences.— The 
Germans have divided all sciences into the liberal and the 
lucrative. The former are supposed to have no iuimediatc 
bearing on any bread-winning profession, but to be studies 
belonging in a scheme of liberal or general education. The 
latter, called die Brotivissoiscliaften, — "The Bread-and- 
Butter Sciences, " — include those studies that are immediately 
preparatory for some lucrative business or profession. 

From what has been said above, it is evident that, strictly, 
no such arbitrary division of studies can be made; for culture 
studies of every kind have a practical material value. 
Training and discipline, without regard to the study that 
furnishes them, have the effect of making it easier for a man 
to earn his living; that is to say, every study belongs in some 
sense and in some measure among the lucrative sciences, 
and among the liberal sciences as well. Whatever enlarges 
a man's mental horizon, whatever gives increased precision 
and power to his faculties, has value both practical and disci- 
plinary. It should be noted, however, that the material or 
lucrative value sought by means of the practical or so called 
lucrative sciences is more immediate and definite than is 
aimed at in the case of the liberal sciences. Liberal culture is 
primarily culture for its own sake; but the training has a 
remote value in heightening the efficiency of its possessor in 
meeting the unforeseen and multiform requirements of life. 
It ecpiips him with 2i general preparedness for life's activities 



16 PEDAGOGICS OF GEOGRAPHY. § 5 

even more valuable in a money point of view than does pro- 
fessional training. The man whose powers are all in a con- 
dition of high development and training can adjust himself to 
almost any position in life, and by his culture and acquired 
habits of mastery and easy comprehension, he has a power 
of adapting himself quickly to new requirements. The 
strictly professional man cannot do this. If a lawyer is 
debarred from his practice, he is likely to be ineffective every- 
w^here else. We have a good example in the destruction of 
the business of wood engraving by the discovery of the 
' ' new-process " engraving. Thousands of persons that spent 
years in acquiring expertness in the supplanted art find 
themselves compelled to do something else; and their diffi- 
culty in adapting themselves to a new work is generally 
greater in proportion to their skill in their former work. 

The very best phase of special training is that based on 
wide general culture. Education, for what Herbert Spencer 
calls complete living, comprehends not only the widest range 
of liberal culture of which the faculties are capable under 
existing circumstances, but also minute and thorough training 
in some useful art or profession. Now the five general groups 
of studies mentioned are all indispensable to a liberal educa- 
tion, and equally so to a profession. Some one says that a 
lawyer and a teacher should know everything, and the same 
may be said of pretty nearly every other profession when at 
its best. In a liberal education, the wider and more com- 
plete the mastery and coordination of its component subjects 
of study, the broader and safer will be the substructure it 
will furnish for a special profession. 

11. Educational Tlieovy As Modified by Educa- 
tional Fact. — Every person that has been engaged in the 
activities of life has learned that theor}^ and actual practice 
must differ widely. However complete and plausible a plan 
may seem, it must be subjected to the test of a trial before 
it may safely be accepted; and to this fact must be attributed 
the wise and cautious conservatism of the man of wide 
experience. The ready acceptance by the ignorant and 



§ 5 PEDAGOGICS OF GEOGRAPHY. 17 

inexperienced of each "fad" and "ism" is to be accounted 
for by the fact of this same condition of ignorance and inex- 
perience. The alert business man, who has been engaged 
for years in discriminating between shams and realities, 
never sends one dollar in answer to an advertisement that 
promises him for that sum a watch " really worth twenty 
dollars." He has learned that nobody in this world system- 
atically gives something for nothing, and that promise is 
one thing and performance quite another. The old criminal 
lawyer and the experienced detective are each prepared to 
doubt appearances and to insist on the test of absolute 
evidence. In every department of life, ingenious persons 
are engaged in causing things to seem veiy different from 
what they are in fact. We are constantly tempted to place 
value on things without value, and the teacher does not 
escape the error of putting undue stress on theories that 
have never been tested. It is comparativel}^ ea.sy to outline 
a theory of education that seems to be perfect, but to work 
it out in practice is not so easy. In one place at aparticulai- 
time it may be satisfactory, excellent, or a failure; elsewhere, 
or under other circumstances, it may yield results entirelv 
different. Training in its best sense is not something that 
has a definite beginning and end; it is a condition of growth 
that begins before the cradle, and is perhaps not finished 
at the grave. 

"When would 3^ou begin the process of educating a child? " 
is asked of one of our wisest thinkers. "Not less than a 
century before his birth," he replies. 

The lines along which individual educational progress is 
made most rapidly and easily may be laid down so as to 
accord with average conditions. Dr. Harris has done this, 
as have also many others; but in attempting to realize these 
schemes by actually working them out, we are confronted 
with the fact of "many men, many minds." The native 
vigor and the functional efficiency of faculties both mental 
and physical are not the same in those whom we would 
educate. It is soon discovered that for each kind of 
growth, the food and excrci.se that are good for one per.son 



18 PEDAGOGICS OF GEOGRAPHY. § o 

are usually hurtful to another. Mental predispositions and 
aptitudes differ, and must be taken into aecount. Of one 
pupil we may make a linguist but not an artist; of another, 
a mathematician but not a scientist. These individual pre- 
dilections sooner or later determine particular directions of 
individual culture, and defeat every attempt to make it 
all-sided. 

Hence, the educational value of any subject of study 
depends, among many other things, on the bent or inherited 
tendency of individual powers. When to these personal 
likings and aptitudes we add those involved in external cir- 
cumstances, it becomes clear that educational valuation is a 
complicated and difficult matter. No one would assert that a 
course of study could be arranged so as to give the best pos- 
sible result at once for the savage and the civilized, for the 
Mohammedan and the Christian, for the peasant and the 
prince. 

13. Appi'oximation in T^dncatioii to Averag'e 
Requirements. — Obviously, then, it is impossible to estab- 
lish any general curricuhnn that shall have equal and con- 
stant value under all circumstances. It is equally clear that 
methods of teaching are as much dependent on circumstances 
for their value as are the matters taught. On account of 
the magnitude of the work, however, some approach to 
general treatment must be made. When the children of 
a nation are to be educated, it is impossible to specialize the 
work of teaching so as to make it accord with the individual 
wants and aptitudes of pupils. In our public schools, the 
best that can be done, perhaps, is to meet, as nearly as pos- 
sible, general or average needs. It follows, therefore, that 
the determination of approximate educational values is a 
matter of extreme importance. This is especially the case 
in the elementary schools, in which the great mass of chil- 
dren are found, and beyond which only a small percentage 
of them go. In the secondary school and in the college and 
university, there has been, within the last decade, an increas- 
ing specialization, so that nearly all our high schools and 



§ 5 PEDAGOGICS OF GEOGRAPHY. 19 

academies have several elective or optional courses, with 
opportunities of choosing in these courses particular subjects 
in varying degrees of completeness. In this city, for example, 
our high school has five courses to choose from. These courses 
are as follows: Classical, Latin-Scientific, Scientific, English, 
and Commercial. There is besides a Normal Training course 
with a department in Kindergarten instruction. So that 
in our higher — our secondary — schools the predilections of 
students and the practical end for which a given study is 
pursued become elements that are available in estimating 
educational value. Whether this opportunity of choosing the 
subjects that make up the course pursued by our children 
will ever be extended to the lower schools, or whether it 
should be so extended, is doubtful. Indeed, schools below 
the secondary usually aim to teach but little more than the 
rudimentary subjects, without which nothing higher can be 
understood. It is only of late years that this fundamental 
work has been increased by the addition of drawing, cook- 
ing, sewing, inventional geometry, manual training, color 
study, lessons in the elements of various sciences, callisthen- 
ics, music, the effects of stimulants, and many other matters. 
Concerning the wisdom of making some or all of these a 
part of the work in our elementary schools, there are many 
conflicting opinions, and each subject has its advocate skilled 
in special pleading. But this is a matter that need not be 
discussed in this Paper. The thoughtful teacher knows that 
a wise conservatism is indispensable to steadiness and eifect 
in working towards any object, and that on the person offer- 
ing anything new or asking a departure from that w^hich is 
established, lies the obligation of proving that it is necessary. 
Many things may be extremely useful, indispensable, indeed, 
under certain circumstances, and yet, under other conditions, 
be worthless, nay, even harmful. In education, as in most 
other matters, there is a place for everything that properly 
belongs to the subject, and for each item that helps to make 
up the general scheme there is a due measure and propor- 
tion of value. 

In passing, it is important for the student to note that, 



20 PEDAGOGICS OF GEOGRAPHY. g 5 

almost without exception, the additions that are made 
from time to time to our school curricula are in the direc- 
tion of the practical. They belong to the lucrative and 
not to the liberal studies. Indeed, the present tendency 
in education is almost wholly towards a greater attention 
to those studies that are directly concerned in the more 
rapid accumulation of wealth, and in increasing the output 
of products that are important to man's physical comfort 
and well-being. 

13. Causes on Wliicli the Value of Geography 
Deijends. — Three-fourths of a century ago, geographical 
science was in its infancy. Bryant, in his "Thanatopsis," 
which he wrote about 1820, has the following expression of 
geographical remoteness and inaccessibility: 

Take the wings 
Of morning, pierce the Barcan wilderness, 
Or lose thyself in the continuous woods 
Where rolls the Oregon and hears no sound 
Save his own dashings 

The horizon of men in general was then very narrow. 
The rivers that were navigable for "arks," rafts, and flat- 
boats were almost the sole avenues for such rudimentary 
inland commerce as there was in those days. The tribes of 
ancient Gaul, of whom Caesar speaks in his " Cominen- 
taries," were nearly as well served by merchants as were our 
people a century ago. The railway and the locomotive were 
unknown in this country, for the first locomotive ever con- 
structed was completed in 1.S24 in England, and the first 
railway for locomotion by steam power was opened between 
Stockton and Darlington on September 27, 1825. Every- 
thing connected with it was crude, and it was for a long time 
engaged in proving its right to be, and in winning the reluc- 
tant aid of capital. If, within a week after printing, a news- 
paper was delivered at a point two hundred miles away, the 
feat was regarded as an instance of marvelous promptitude 
and enterprise. The news it contained was local, and not, 



§ 5 PEDAGOGICS OF GEOGRAPHY. 21 

as now, fresh from every important place. Timbuctu and 
Lhasa are less remote now from the resident of interior 
Pennsylvania than were Philadelphia, New York, or Balti- 
more in those days. 

It is useless to dwell on the changes since. vSuffice it to 
say that the study of g-eography in our schools has been made 
a necessity. Geography began with the first wanderings of 
men from the place of their birth, and each added facility for 
intercommimication has served to heighten mere interest in 
place knowledge into utility and final necessity. Nation after 
nation has established bureaus for accurate survey, until now 
it is difficult to indicate a spot of the habitable globe that 
has escaped the chartographer. Wherever the commerce of 
the world has gone, the surveyor and the scientific observer 
have promptly followed. The importance of geography has 
become greater with every step in the civilizing- of the world, 
and it is coming to be a material omission in one's education 
if he is ignorant of geography. Only about a score of years 
ago John Stuart Mill wrote of the slight value resulting from 
the study of geography, and a committee on school studies in 
one of our largest cities pronounced it a waste of time to 
study the subject. Nothing of the kind is heard now. 
Geography has come into our school curricula to stay. It 
has made for itself a place of importance equal to that of 
arithmetic, or nearly so. For its increased value it is 
indebted to many influences — the railroad, steam navigation, 
electricity, the newspaper, the camera, commerce, with the 
accompanying efl^orts to colonize, and the labors of civilized 
nations to remove obstacles from the path of commerce by 
indicating exactly where and what they are. As the years 
of development of the earth's resources go by, this interest 
in geographical science will increase. What intelligent 
citizen of our country is not now a ready and eager student 
of every source of information about our newly acquired 
territory ? 

14. Di-. IIari'is''s Estimate of tlie ^'altie of Oeog- 
rapliy. — In his general survey of educational values. 



22 PEDAGOGICS OF GEOGRAPHY. § 5 

Dr. Harris assigns an important place to geography — the mas- 
tery over place. It should be remembered, too, that this was 
done at a time when educators were still disputing whether 
geography has any value entitling it to a place among the 
studies pursued in our public elementary and secondary 
schools. His estimate in general terms is as follows: 

Geography localizes. By its mastery, man comes to realize his 
spatial relation to the rest of the world. As civilized man, the supply 
of his wants of food, clothing, and shelter is a perpetual geographical 
process, realized through a division of labor and commercial exchange. 
By this geographical relation, each individual becomes participant in 
the entire production of the globe, and in turn contributes to all. In 
geography, the child learns this fact of interdependence and com- 
munity, which is, even when known particularly, and not generalized 
by him, of the greatest possible importance as a category in his view 
of the world. It is the second window of the mind. Through it he 
learns of the organic world and its relations to the hiiman race and to 
himself individually. Climate, surface, plants, animals, man, are the 
topics to which he is introduced, and these are general categories or tools 
of thought, the mastery of which gives him great vantage ground. 
Think of him as not possessed of these distinctions in his mind, and see 
what imbecility would result in dealing with the world. Shut up the 
geographical window of the soul, and what darkness ensues. From 
this study, branch out in higher education the special organic sciences, 
meteorology, geology, botany, zoology, ethnology, sociology, and to 
some extent, political and religious forms. 

15. Ps.vcliolo;2:ical A'alixe of Geograpliical Study. 

Beyond the effect of geography in widening and liberalizing 
man's view of the world and its contents, and in furnishing 
him with categories of thought, Dr. Harris says nothing of 
the immediate psychological value of this study. And yet 
tliis is by no means slight or unimportant. A look out of the 
"geographical window" always produces many and great 
changes upon the observer — the mind within. The first and 
most obvious benefit is that of virmory trai)iing. The physi- 
cal and political features of the world pass in review before 
the mind. The student learns their names and their dis- 
tinguishing characteristics. It is as if he becomes a traveler — 
like Ulysses, "a man of many turnings, who suffered much, 
saw the cities of many men, and understood their minds." 



§ o PEDAGOGICvS OF GEOGRAPHY. 23 

All of this he does in iniat^-ination, and so doing strengthens 
the reproductive faculties — the uicniory and the vision poi^'cr 
of the mind. This diversity arouses inquiries about causes 
and effects, and an irresistible desire to classify and reduce to 
unity. To him the winds blow and the sun shines with new 
significance; the mountains are no longer merely something 
that he must cross in his travels; they are obstacles in the 
march of empire, conservators of the peace of the world ; they 
temper the winds, modify the rainfall, and ai^e instrumental 
in determining flora, fauna, the food supply, the climate, and 
the commerce of nations. 

In his imaginary travels he becomes cosmopolitan; his 
T7^'ci'.s- are enlarged and liberalized, his data for intelligent 
judgment are increased, his taste is refined, he gets out of 
and away from himself. The distinguishing- colors and lan- 
guages and manners of men lose their strangeness — their 
^^///rt' character — and he learns to think of men as belonging- 
to one common brotherhood, and learns that, in a sense 
larger than national, individual happiness is an element in the 
weal of the world. ]\Ian's mind, like the lever of Archimedes, 
must have a place where it may rest; as Dr. Harris says, 
it must have a "mastery of place." If one is confined for 
life to the village or the farm where he and his ancestors 
were born, and if there be no means of reaching the summits 
that enclose him, whence he may "clarify his eyesight," and 
his soul-sight as well, with a glimpse of the wider realm 
beyond, his culture will be narrow, his sympathies shrunken. 
A Gerrnan student is not regarded as fully educated and 
ready to discharge the duties of actual life until he has 
traveled. Accompanied by his tutor, he sets out on foot 
with his alpenstock to see at least a portion of Europe, and 
some of its activities. What he is to learn, geography 
teaches, but less vividly. He aims to see the reality, for 
geography shows him only the reflection — the shadow of 
things as they are in fact. His travels will give a sense of 
certainty, of reality, with reference to the actualities of the 
world, and will put into his theories and his book training 
the leaven of a rudimentary experience. His judgments 



24 PEDAGOGICS OF GEOGRAPHY. § 5 

will be corrected, informed, and widened; his material for 
inductive and deductive reasoning about the world and its 
contents will be increased, and liis taste refined, by his 
observations of men and their doings. Indeed, there is 
scarcel}'' a faculty that is not bettered by the study of geogra- 
phy. The Committee of Fifteen places its value next to 
that of arithmetic among the studies of the elementary 
schools. 

IG. Estimate by the Conmiittee of Fifteen. — In 

February, 1893, a committee of fifteen persons eminent in 
the educational work of this country was appointed by the 
Department of Superintendence of the National Educational 
'Association to consider and report upon the subjects of 
study and the methods of instruction of the elementary 
schools. The report of this committee was submitted to 
the Department of Superintendence at its meeting in Cleve- 
land in February, 1805. Its report was one of great impor- 
tance, covering the entire work in the elementary schools 
with respect to both matter and method. The following is 
the part of their report that refers particularly to the educa- 
tional value of geography: 

The educational value of geography as it is and has been in elemen- 
tary schools is obviously very great. It makes possible something like 
accuracy in the picturing of distant places and events, and removes from 
the mind a large tract of mere superstition. In these days of news- 
paper reading, one's stock of geographical information is in constant 
requisition. A war on the opposite side of the globe is followed with 
more interest in this year than a war near our own borders before the 
era of the telegraph. The general knowledge of the locations and boun- 
daries of nations, of their status in civilization, and their natural 
advantages for contributing to the world market, is of great use to the 
citizen in forming correct ideas from his daily reading. 

The educational value of geography is even more apparent if we 
admit the claims of those that argue that the present epoch is the 
beginning of an era in which public opinion is organized into a ruling 
force by the agency of periodicals and books. Certainly neither the 
newspaper nor the book can influence an illiterate people ; they can 
do little to form opinions when the readers have no knowledge of 
geography. 

As to the psychological value of geography, little need be said. It 



§ 5 PEDAGOGICS OF GEOGRAPHY. 25 

exercises, in manifold ways, the memory of forms and the imagination ; 
it brings into exercise the thinking power in tracing back towaixls unity 
the various series of causes. What educative value there is in geology, 
meteorology, zoology, ethnology, economics, history, and politics is to 
be found in the more profound study of geography, and, to a propor- 
tionate extent, in the study of its merest elements. 

Tlie student will of course perceive that the foregoing is a 
very rapid and general statement of the value of geograph- 
ical study. There are many phases both practical and 
psychological that are not touched upon here. The main 
thing has been accomplished, however, in stating the wide 
and growing usefulness of geography, and in urging the 
strong imperative that rests upon the teacher of knowing 
the subject thoroughly and of teaching it skilfully. He 
must be familiar not only with the names and locations of 
capes and bays and rivers and cities, — the mastery of place,— 
but he must be expert also in the philosophy of geography. 
Not as one stitdies Homer's " Catalogue of the Ships " must 
geography be sttidied; it must be understood and taught in 
its causes and effects, its inductions and relations, its changes 
and developments. It is not a study for the memory 
merely, but for the betterment of every faculty, and for 
enhancing the chances of practical success in the struggle 
for place and opportunity in life. Moreover, it is a subject 
that will gain in value from year to year as the resources 
of the world are gradually developed, and as its products 
become more and more widely necessary in supplying 
human wants. 

Every improvement in the means of intercommunication, 
every line of steamers added to the commerce-bearing fleets 
of the world, every extension of railroad into new regions 
or partially developed areas, eveiy invention, scientific dis- 
covery, and exploration; the conflicts of civilization with 
savage or semisavage races, every newly developed need of 
progressing man, together with every device for meeting 
it — all these and innumerable other matters not now dreamed 
of will give additional impetus, importance, and educational 
value to the study of geography. 



26 PEDAGOGICS OF GEOGRAPHY. § 5 



GEOGRAPHICAL MATTER. 



D1VI8IOXS a:nd definitions. 

1 7. Tlie Term •■'■ Geog-raphy." — -The Greek word y^ugc, 
meaning' "the earth," is compounded with other Greek 
words to form the names of various sciences. Each of these 
treats of the earth considered in some one of its many aspects. 
Thus, yi] with da/w, data, "to divide," forms geodesy; with 
Xoyo^, logos, "a discourse," we get geology; yrj compounded 
with voiioq, nojiios, "a law" or "rule," gives geonomy; the 
same word with yi'wafc, g/n>sis, "knowledge," yields geognosy; 
f^tsTQov, metroii, "a measure," and ygdcpi,), grapho, " I write " 
or " describe," when combined with the word for earth, form, 
respectively, geometry and geography. 

The literal meanings of these terms do not indicate with 
any degree of exactness the distinct field covered by each 
science. Thus, there is nothing in the literal meaning of 
geology and geography to show that the former takes account 
of the constitution and structure of the whole earth without 
noticing its organic products, and that the latter is con- 
cerned only with certain phenomena on the earth's surface. 

Of all these terms, geometry is the oldest. It was first 
used among the early Greeks in the sense of a ineasurenie)it 
of land; a geometer was, therefore, a mere surveyor as we 
now imderstand it. The word did not take on its exclusively 
mathematical sense until within a comparatively recent 
period. In the middle ages, what we now call geography 
was regarded as a part of geometry. What was then meant 
by geometry was an abridgment of Pliny's geography ; and 
this was supplemented by definitions of some of the most 
common geometrical forms. 

The subject matter of each of the sciences mentioned 
above is determined, when determined at all, by convention 
— a kind of vagiie general agreement — something that does 
not remain constant for any considerable time. As the 



§ 5 PEDAGOGICS OF GEOGRAPHY. 27 

domain of a science is enlarged by new investigations and 
discoveries, it is usually subdivided into more definite and 
less comprehensive branches, for which new names are 
devised. Something similar to what in human industry is 
called " division of labor " takes place here; and it is impor- 
tant that the teacher of a particular subject should know 
its scope and comprehension. He should be familiar also 
with the relations of each subject that he teaches, to every 
other subject considered as belonging to his professional 
work. He should know its time and place in a general 
scheme of culture, and should have definite notions of its 
educational value. Such knowledge should pi"event him 
from emphasizing too much or too little any subject in the 
curriculum that he follows in his work. 

18. Definition of (;e«),i»rai)li.v. — In its literal or etymo- 
logical sense, geography is a description of tJic earth. But 
there are many aspects in which the earth may be described; 
and of these, some are recognized as properly belonging in 
the textbooks intended for use in our schools, and others are 
not so recognized. It has, therefore, been necessary to 
narrow this wide generic meaning of the word geographv, 
and to include only those phases of the subject that have 
been found to have general value either in practical affairs 
or for purposes of discipline. In this restriction of geograph- 
ical matter, the earth as a luhole does not usually receive 
much attention, at least in textbooks intended for elementary 
and secondary schools. That phase of the subject, compre- 
hended under the division of uiathematieal or astroiiomieal 
geography, is made prominent in navigation, astronomy, 
geodesy., and some other sciences. With the exception of 
such limited consideration of the earth as a planet as is 
required in order to understand latitude and longitude, the 
seasons, day and night, the tides, and some of the phenomena 
of meteorology, it is the surfaee of the earth that engages 
the attention in our works on geography. 

In seeking for a satisfactory definition of geography, it 
soon becomes apparent that the task is not easy. The old 



28 PEDAGOGICS OF GEOGRAPHY. § 5 

definition, " Geography is a description of the surface of the 
earth," is faulty because it is so extremely general. It is a 
mere translation of the Greek words that compose the term. 
When, however, the attempt is made to be more explicit, 
and to indicate just what should, and what should not, be 
treated in the science, and thus to meet the requirements of 
a perfect definition, it is seen that what is true of many other 
sciences is true also of geography — it cannot be adequately 
defined. 

One of our latest and best authorities gives the following 
definition, or description : 

' ' Geography is the science that describes the surface of the 
earth, with its various peoples, animals, and natural products. " 

This is in no respect better than the old definition quoted 
above, if, indeed, it is so good. We have here an example 
of an attempt to define that which, while incapable of exact 
definition, may nevertheless be imderstood well enough for 
all requirements in teaching and studying it. And the fact 
is that most of the latest and best geographical textbooks 
make no attempt to define the science. 

19. Tlie Element of Place hi Geograpliy. — At first 
sight, geography seems to be a confused mass of incoherent 
details — an inextricable tangle of facts without sequence or 
relation. In the confusion of history, events maybe con- 
sidered in the order of time, and in the relation of cause and 
effect ; but neither these principles nor orderly arrangement 
and classification furnish much help in dealing with the facts 
of geography. Here the conspicuous category \s place ; but 
this is the case with every science that deals with material 
things or their relations. Indeed, for everything of which 
we can think, the mind demands that there shall be definite 
location. All the natural sciences, as well as the industrial, 
political, and social sciences, owe their divisions, subdivisions, 
'classifications, and their chief interest to place and environ- 
ment. Place is one of the most important of Aristotle's ten 
categories of thought — one of the conditions necessary in 
order that we may predicate. 



§ 5 PEDAGOGICS OF GEOGRAPHY. 2'.) 

Every science, therefore, involves something of geography 
— something of the mastery of place — but each should have 
some other dominating interest in order to give it scientific 
unity and logical order. And the fact is that every science 
does have some such principle of interest and arrangement. 
In geography, however, place is so conspicuous and so impor- 
tunate as to obscure every other element of order. Neither 
the textbook on geography nor the teacher of the subject can 
easily escape from the thraldom of mere location. And, 
worst of all, the results to the student are the study and 
remembrance of mere names and markings on maps instead 
of the acquirement of correct concepts of real earth features. 

30. Abuse of the Idea of Place. — The answer to the 
question Where ? is undoubtedly of much importance in the 
study of geography; but while this is true, the predominance 
of mere place in our conception of things has led to a great 
deal of unsatisfactory work in our schools. It has resulted 
in a kind of teaching in which the highest aim consists in a 
fixing in the mind of mere position on maps, and in the 
memorizing of accompanying names. To bound political 
divisions, locate capitals and chief cities, and mention in 
some prescribed order the natural features of land and water, 
came to be the chief requirements of place geography. The 
teacher that could rapidly and certainly secure glibness on 
the part of his pupils in such requirements was assumed to 
have done his work well. There were, in the days of this 
kind of teaching, few pedagogical critics of matter and 
method to raise awkward questions of educational values or 
to inquire too closely into the real nature of the geographical 
concepts produced by this kind of teaching. Those were the 
innocent days of the golden age of geographical teaching, 
vvdien the facts of the science were expressed in lines such as 
might be adapted more or less easily to some familiar tune 
that the students could sing. 

Capital of Maine, Augusta, 

On the Kennebec River; 
New Hampshire, Concord, 

On the Mcrrimac River. 



30 PEDAGOGICvS OF GEOGRAPHY. § o 

This kind of thing" extended so as to include all the states 
then composing the Union, the countries and capitals of 
Europe, and the principal rivers of the grand divisions; 
these, with many other items of equal' importance to success' 
in life, formed a large part of geographical teaching not so 
very many years ago. For a student to be able to sing all 
the geography that had been tortured into a shape partially 
rhythmical, was evidence of scholarship as generally recog- 
nized and respected as was the ability to spell all the hard 
words in the extant spelling books. There were in those 
days no impracticable examiners or county superintendents 
that insisted upon knowing exactly what a capital is; none 
that persisted in questioning about it until they left the stu- 
dents in doubt as to whether a capital is something good to 
eat or is only a kind of mineral dug from the earth. 

This is the geography that some of our fathers learned, 
and, from some evidences, it is not unknown even now in the 
actual work of many of our schools. This conception of 
geography owes its wide prevalence and its long endurance 
to the fact that place is so obvious and constant an element 
of all data in the study of the earth. 

31. The TJelatiou of Science to ITiinian IN"eecls. 

Few of the sciences are studied for their own sakes and 
without some ulterior purpose. The various branches of 
mathematics, for example, are pursued partly because of 
the excellent mental discipline they furnish, but chiefly 
because of the power they give man over his environment. 
They furnish him with the lever with which he moves the 
world. History, by revealing to him the wonders that men 
have done, suggests the wonders that man may do here- 
after; and this is one of its highest claims to a place 
among the sciences. The physical sciences, like the mathe- 
matics, are valuable, not merely for training- the mind, but 
in that they lay bare for human advantage the secrets of 
nature, converting her forces from agencies of malevolence 
into such as make for our weal. Natural phenomena no 
longer suggest the impending and unappeasable hostility of 



§5 PEDAGOGICS OF GEOGRAPHY. 31 

some concealed malevolent divinity ; but, rightly under- 
stood, they are the manifestations of forces that may be 
made to contribute in rendering easier man's struggle for 
existence. The lamp of science has its gcnic whose service 
to man is hurtful or helpful according to the intelligence 
with which its potencies are directed and understood. 

This same helpfulness should characterize in some measure 
every science that can engage the attention. They should 
all have as a primary object the enhancement of human wel- 
fare. And the fact is that any science worthy of the name 
does have this relation to the wants of the race. On the 
earth, man is the object of central interest. His needs of 
every kind — physical, mental, moral, esthetic, and spiritual 
— are clamorous for their appropriate means of satisfaction; 
and the overshadowing purpose of every science is to indicate 
the line of least resistance to the attainment of this satisfac- 
tion. As man's wants increase in variety and complexity, 
the sciences increase in munber and scope, and each one 
addresses itself to the task of furnishing a definite answer as 
to the best and easiest way of satisfying human desire for 
something better and higher. Any science, therefore, or 
any phase of a science that does not have this object in con- 
templation is deservedly neglected. The old question of 
cui bono .^ — what is it good for ? — is asked with respect to 
every subject propo.sed for investigation; and unless it can 
be .shown to be of probable and not too remote value toman, 
it is passed over or rejected. This requirement is especially 
insisted upon in the case of every subject offered for incor- 
poration in a course of study; for here its purpose is to train 
our children for the ■ places they will probably occupy in 
actual life. 

33. Test of ^"aliie in Geograpliical Matter. — It would 
appear, then, that the educational value of every science 
depends upon the measure of its usefulness to man, and not 
upon anything inherent in the science itself. This criterion 
of value has been steadilv gaining in recognition during the 
last score of years, until now we constantly speak of this as a 



32 PEDAGOGICS OF GEOGRAPHY. § 5 

utilitariaji age — an age when the right of any science even 
to be, is determined by its possible usefulness. Usefulness 
for what ? For man, " the sum and crown of things." Any 
subject possessing nothing more than mere scientific or doc- 
trinaire interest, with no other particular value or useful 
application, commands no serious attention. 

The application of this test to the subject matter of geog- 
raphy was made long ago by Ritter, von Humboldt, and 
other scientists. They believed that "on earth there is 
nothing great but man," and it was an easy inference that 
those aspects of the science that are most helpful in perfect- 
ing the totality of man's powers are the aspects that should 
have greatest prominence in any scheme for man's culture. 
Moreover, it is not man as a thinking being alone that was 
consideredin this adjustment of culture to actual need, but man 
as an inhabitant of the planet, man in the sum of his various 
powers and relations. These scientists had in mind man's 
"complete living," and their aim was to omit nothing that 
would contribute to human efficiency, man being regarded as 
a force acting upon the world about him. 

It will be observed, therefore, that in selecting and 
arranging the materials to make up a course in geography 
that shall be the best possible — ^rational, coherent, and defen- 
sible — this is the test of value — available usefulness to the 
student in his probable future enviroinne)it. Hence, the 
inquiries that the teacher should address to himself concern- 
ing any subject he proposes to teach are: "Just what good 
in the future will a knowledge of this subject do for my 
pupils ? In what way will it effect this good ? Can the 
same object be attained as well or better in some other way ? 
Will the proposed attention to this subject involve the entire 
or the partial neglect of something still more important ? " 
He should insist upon a due proportion of parts in his work, 
a definite end to be reached by each separate item, and a 
clear vinderstanding of why such end should be sought. 
Moreover, he should fix upon a distinct plan of procedure, 
making very sure that it is the best, and then he should 
work steadily and persistently along the easiest lines leading 



§ 5 PEDAGOGlCvS OF GEOGRAPHY. ;;:, 

to his preconceived object. Mnch of the poor work done in 
teaching is owing to its desultory haphazard character, and 
to an absence of proportion in estimating educational value. 
The principle of selection indicated above is general. It 
is applicable not onl}' to geographical .science, but to every 
other subject worthy of a place in any scheme of human cul- 
ture. One of the ancient schools of philosophy taught that 
'' man is tJic incasurc of the universe ^^ — that things finite arc 
to each man what the}' sccui to him. In other words, every- 
thing is relative to our faculties, and is not a fixed reality, 
having an independent existence. However this may be, it 
is certain that, in a similar sense, there is no such thing as 
value except that which is owing to the mediate or immedi- 
ate fitness of things for the gratification of our wants. This 
criterion of educational- i;tility should be very distinct in the 
mind of the teacher, and should regulate his professional 
work in every subject that he teaches. 

33. General Divisions of Geograpliy. — There are 
many divisions and subdivisions of geographical science. 
These arise chiefiy from the manifold relations of man to 
the world about him, and from the many possible stand- 
points or bases of classification. These various phases of 
the subject are usually indicated by adjectives prefixed to 
the generic term geography. The following are some of the 
most important of these specific terms: mathematical, 
astronomical, physical, political, historical, ancient, com- 
mercial, botanical, industrial, zoological, geological, mag- 
netic, descriptive, topical, comparative, etc. From all this 
confusion it is necessary for the teacher to organize a coher- 
ent outline of the science; for such a general view is indis- 
pensable as a guide in teaching any subject. Without it, all 
sense of proportion and comparative value and importance 
will be ab.sent from the work of instruction; for, while the 
science has many phases, each of paramount concern with 
respect to some particular standpoint, not every branch of 
the subject is vital as part of a course for general training in 
geography. In arranging such, an outline, it must not be 



U PEDAGOGICvS OF GEOGRAPHY. g 5 

forgotten that ///a// is the object of primary interest in the 
science; his wants and welfare, his relations and activities 
should determine the suljstance and propcjrtion of the parts 
as well as their arrangement. 

Now, there are two general aspects in which the earth 
may be studied. These are : 

1. T/w cartJi as a ^^'hoU\ or in itself. 

2. The car til as tlic abode of life. 

34. The Kartk ^V.s ji Whole. — These two aspects of the 
study of the earth include under them all the subdivisions of 
the subject that are referred to above. Out of the first, 
which regards the earth merely as a planet having a certain 
shape and surface structure, and certain positions and motions 
wdth respect to the sun and moon, arise mathematical or 
astronomical geography, physiography, or a description of its 
surface features {(jivaic, pliysis, "nature"), and physical geog- 
raphy. This last is based npon physiography, of which it 
is the scientific extension, and its province is to note and 
give a scientific account of the phenomena and the changes 
upon the surface of the earth. This distinction between 
physiography and physical geography is one of importance 
to the teacher, and should be distinctly and exactly under- 
stood. It is analogous to the difference between anatomy 
and physiology, the first of which deals with mere structure, 
while the latter is concerned with function^ purpose, and 
laios. Physiography regards the natural features of the 
earth — the variety, arrangement, and relations of its land 
and water features, its relief, its coast lines, and its systems 
of mountains, plains, and valleys. It considers 'only what 
is, not what Jiappciis. Physical geography continues the 
study by considering the earth as an (n\ganism in which 
change is going on, where life resides, and forces are oper- 
ating in accordance with physical laws. It investigates 
those changes in their causes and eft'ects, notes the relation 
of that resident life to those varied forces and physical con- 
ditions, and formulates the laws by which the whole complex 
oreanism is controlled. 



§5 PEDA(U)(;iCvS OF GEOGRAPHY. 35 

25. The Karlli As the Abode of Lile.— It is from 
regarding the earth as the abode of man that seientists have 
been led to make most of the subordinate branches of geog- 
raphy. Nearly all of these are, however, mere si:bdivi- 
sions of physical geography. The human requirement for 
food, clothing, shelter, education, progress, government, 
and social intercourse has led to the development of a 
separate branch of geography, and out of all these must be 
gathered the material of which to construct a course that 
shall be suitable for a curriculum for general use. The task 
is indeed not easy, and the teacher is called upon constantly 
to distinguish between the essential and the non-essential. 
It is difficult to find two authors that agree in their material 
or arrangement. But the general tendency is towards that 
kind of geographical knowledge that will be most helpful to 
man in the effort to supply his various wants. In other 
words, geography must be regarded as belonging among the 
lucrative sciences rather than among those denominated the 
liberal. At any rate, every teacher should have in mind a 
general outline of the science, as well as a distinct scheme of 
its subdivisions and the considerations to which they are 
owing. Peculiarly apropos here is a quotation from the 
writings of Marcus Aurelius, the Philosopher Emperor of 
Rome ; 

Make for thyself a definition or description of the thing that is 
presented to thee, so as to see distinctly what kind of tiling it is, in 
its substance, in its nudity, in its entirety ; and tell thyself its proper- 
name, and the names of the things of which it has been compounded, 
and into which it will be resolved. For nothing so elevates the mind 
as to be able to e.\amine w'ith method and truth every object that is 
presented to thee in life, and to look at things always in such way as 
to see what kind of universe this is and the use everything performs 
in it, and what value everything has with respect to the whole and 
what with reference to man, who is a citizen of the highest city, of 
which all other cities are like families ; wdiat each thing is, and of what 
it is composed, and how long it is the nature of this thing to endure. 

In other words, we should study things both in them- 
selves — their essence — and in their relations; and this is a 
special necessit}' with him that would be a teacher. 



oO 



PEDAG()(;iCvS OF GEOGRAI'llY. 



S 



I. L\ Itself 



36. A Fiindamentul Outline of Oeograi>liy. — It is 

believed that the following" general view of the scope of 

geographical science will be found useful to the teacher. It 

does not, however, aim to show all the subdivisions of the 

subject, nor the details of a course suitable for actual use in 

the schoolroom. It is merely a comprehensive view such as 

every teacher should have in his mind as a basis of intelligent 

work. 

' 1. As a JfV/r^A'.— Mathemat- 
ical Geograph}-. 

//s Features. — Physiog- 
raphy : Descriptive or 
Topical. 

Its Sia'facc Changes. — 
Physical Geography. 

Vegetable Life. — Botan- 
ical Geography. 

Annua/ Life. — {a) Ani- 
mals in General. — Zoo- 
logical Geography. 
{b) Man. — Ethnography: 
Political, Industrial, and 
Commercial Geography, 
etc. 



Tlie Earth 



II. As AiiODE OF Ln-E 



3 7 . Ultimate Basis of Science. — In the teacher's search 
after a clear notion of the causes that underlie all physical 
change on the earth — life in all its phases — he can scarcely 
escape the greatest of all the inductions of science. This 
induction is that solar energy is the primary and sole cause 
of motion upon the earth, and, therefore, of all terrestrial 
life and thought. Physical science, and, in its last analysis, 
all science, is only an orderly accomit of the enormous and 
complicated activities produced by the Ave principal forms 
of energy, gravity^ cJicmical affinity., electricity, magnetism., 
and Jieat ; and, for our system, the great reservoir and source 
of these energies is the sun. To these energies are owing 
all the movements of air and water, the disintegration of 
rocks and mountains, and the formation from them of the 
broad plains whose fertility feeds the world. 



§ 5 PEDAGOGICS OF GEOGRAPHY. 37 

j\Ir. Tyndall. in his " Heat a JModc of i\I(jtion," shows that 
heat and motion are only different names for the same thin^i;-; 
that eoohng is diminution of motion and heating is aeeelera- 
tion of motion. He and many other scientists have abun- 
dantly proven the beautiful generalization known as the 
"Correlation and Conservation of Energy." This doctrine, 
of which no teacher can afford to be ignorant, maintains that 
all varieties of energy are interconvertible and indestruc- 
tible. A certain amount of heat can be converted into a fixed 
amount of motion, light, electricity, or magnetism ; and, 
whatever form it may take, it is incapable of increase, 
diminution, or extinction. And this energy in its myriad 
forms can all be traced to the sun as its source. In order 
to give a notion of the vast amount of this solar energy 
received each day, Mr. Tyndall says that, " if distributed 
uniformly over the earth's surface, it would be sufficient to 
liquet}" a layer of ice 100 feet thick covering the whole earth." 
This enormous contribution reaches the earth and is trans- 
formed for our welfare into an inconceivable complexity of 
motion and life. It is translated into song and laughter and 
life and thought. It is heard in "the complaining brook," 
in the roar of the cataract, and in the majestic bass of the 
ocean. 

38. Physical Science the Essence of Geography. 

With the exception of topography — tliat phase of geography 
in which mere place is the leading consideration — the subject 
consists almost wholly of the inducti(Mis of physical science 
and of the facts that have furnished these inductions. This 
is largely true of physiography, and entirely so of physical 
geography. Commercial geography, including the statistics 
of the industries and of commerce, is only the story of the 
earth's conversion of solar energy into life and motion, into 
forms available for human needs. The .same is true of every 
other branch and subdi\'ision of the subject. And every 
science that deals with li'V, whether vegetable or animal, as 
well as every science that in\-estigates the causes, modes, 
and results of the interplay of forces on the earth, is an 



38 PEDAGOGICS OF GEOGRAPHY. § 5 

element in geographical science. What is known as physical 
science is the very soul and essence of geography. A wide 
philosophical grasp of the subject is impossible in the 
absence of a similar grasp of its component sciences. It 
follows, therefore, that a comprehensive and thorough 
knowledge of nature — of her forces, processes, and laws — 
is a necessary equipment in the teacher of geography. The 
absence of such knowledge, and the impossibility, imtil quite 
recently, of obtaining it, are perhaps the causes for the 
extremely poor work that has been done hitherto in teaching 
geography. Any one that would excel in this work must 
know not only the surface of the earth, but also what is 
occurring there ; he must be familiar with the forces that 
are operating, with the laws that regulate their action, with 
the effects produced by these forces, and the uses to which 
their products may be put. He must be familiar with all 
the wide generalizations of science — he must be a scholar 
and a student. 

This of course is an ideal of excellence that is rarely real- 
ized; but if the writer has made plain the need for it as a 
condition to the best work, his object has been attained. If 
the student has been made to see that the successful teacher 
of geography must be a persistent student of the physical 
sciences, and if he has received an effective impulse to such 
study, there can be little doubt of the results that will 
follow. Read again and again the works of the great 
investigators of nature, and especially the works of such of 
them as have generalized and reduced to scientific form their 
own work and that of others. Remember, too, that no 
normal school, and no process of training, ever did or ever 
can make a great teacher. The great things that have been 
accomplished in the world have been prepared for by self- 
effort on the part of those that achieved them. Self-activity, 
thought, reflection, investigation, experiment — these are 
indispensable to scholarship in science. 

29. Man"* Place in Science. — We have alread}' referred 
to man's importance in the general scheme of things, and to 



§ 5 PEDAGOGICS OF GEOGRAPHY. 39 

the completeness with which his interests and wants over- 
shadow everything else in all systems of education. Goethe 
says, " Man is the most interesting study of man, and should 
perhaps interest him exclusively. Everything that sur- 
rounds us is either an element in which we live or a tool that 
we apply." Here we have a brief and forcible statement of 
the highest criterion of value in education. Alan is " the 
be all and the end all " in this domain. Whatever in science 
has bearing or influence directly or remotely upon human 
welfare or development is educationally \ahuLble; whatever 
is outside of such relationship is to be passed by as worthless. 
By coordinating what has already been said, we may see in 
proper order and relation the entire series of which man is 
the final and most important element. The sun as the source 
of energy acts upon the otherwise dead and inert matter of 
the earth. Vibration, motion, circulation begin, and the 
outcome is life. This at first is the crudest and simplest 
animal and vegetable life; but the long geological story 
begins, and after myriads and myriads of years the culmi- 
nation is man — a being capable of indefinite improvement, 
whose needs, increasing with his development, place all 
science, all art, and all the resources of nature under contri- 
bution. Between the great solar center from which life and 
motion and force flow, and the mind of man, which is the high- 
est expression of life, lies the domain of science. Whence came 
man, and how ? What is he, and what is his environment ? 
Whitherdoeshego? When these questions are fully answered, 
the story of science is fully told. But of these questions, the 
first and the last are incapable of being answered by finite 
intelligence; even the second baffles us in our attempts at a 
complete answer. We see but dimly and partially the mean- 
ing of it all ; but human progress with its newly born m-gencies 
is the unceasing force that impels new inquir}' and awakens 
fresh interest. Man, being the central figure in science, that 
which will give hini mastery over his surroundings must 
be the chief object — the most important end — of education. 
Geography, being the science of man's ]Dhysical environment, 
is the source and framework of all physical science. 



40 PEDAGOGICS OF GEOGRAPHY 



CONCEPTS IN ELEMENTARY SCIENCE. 



SENSATION AND PERCEPTION. 

30. Tliiiig-s Are Distinguished by Difterences. 

Almost as soon as the child arrives in the world he begins to 
observe. This he does by means of the senses — the organs 
of sensation. Each of these, acted on by its appropriate 
stimulus, brings to the mmd reports from the external 
world. The tyes tell of the colors, shapes, sizes, and other 
■z^/i'7^^/ qualities of objects without; the ears report the soho- 
rous phenomena of the world — the chief features in the story 
of its activities, its motions and forces, its changes, its life. 
To the knowledge thus gained, each other sense makes its 
contributions. These phenomena attract the child's attention 
only by the fact of their differences. If there were only one 
color; if the shapes, the sizes, and other phases of objects 
presented no variety; the eyes would be of little use or value, 
and the disadvantag-e of being born without sight would be 
much diminished. Or, if only one unchanging sound met 
the ear during our life upon the earth, we should have no 
use for the organ of hearing. Such uniform imvarying sound 
we should never notice; but if it should suddenly cease or 
should change in some manner, our attention would then be 
immediately attracted by the change — the dffereiiee. Illus- 
trating this fact, some one has made the very curious ob.ser- 
vation that, if one were born with toothache that never varied 
in intensity, and that, if after a time it should leave him 
suddenly, he would then for the first time experience pam. 

Wlien the difference between two objects is very slight, 
they are said to rescjnble each other; when the resemblance 
is very close, there is little to engage the attention; and 
when the likeness is perfect, after a futile attempt to detect 
some point of difference between the objects, all interest 
lapses. One of our thinkers asserts that things are known 
onlv ill /hei/isehes, and i?i their relations to other things. To 



§ PEDAGOGICS OF GEOGRAPHY. 41 

know a thing" in itself is to know such of its (jualitics as are 
impressed upon the mind through the senses; to know it in 
relation is to know how it is conditioned with respect to 
other things — its relative weight, size, form, distance, posi- 
tion, etc. Now, all these forms of knowledge amount, in 
the last analysis, to a perception or a cotiscioiisncss of differ- 
ences. 

31. Need for Sense Training-. — It might at first 
thought seem that all persons endowed with the usual organs 
of sense would reach the same degree of thoroughness in 
knowledge acquired through the senses. Such, however, is 
not the case ; on the contrary, there is an art of seeing and 
of using the other senses of which not even the merest rudi- 
ments are ever acquired by some persons, while others are 
soon known as "trained observers." It is not because of 
superior sense organs that some excel in this matter. Huber, 
the great observer of bees, was blind ; Beethoven was totally 
deaf when he composed his wonderful "Requiem." Sense 
alertness, keenness, and discrimination are partly owing to 
finer brain fiber, but much, very much, to training. This 
art, like every other, is perfected by persistent practice. By 
the long imperative of necessity, development has converted 
the eye of the eagle into a telescope. Here, as everywhere 
else in matters of practice and habit, the maxim of Comenius 
is applicable, " We learn to do by doing." 

Every teacher should be familiar with Mrs. Barbauld's 
well known story, " Eyes and No Eyes, or the Art of See- 
ing. " Read by a child, it furnishes him an unrivaled incen- 
tive to observe, to reason about what he sees, and to 
generalize and classify. As a mere boy, I read it many years 
ago, and I shall never forget the impression it made upon 
me. Even now the twitter of a bird in a thicket sets me to 
wondering what " tragedy of the woods" is going forward. 
A walk in the fields or woods will have the " museum charm 
and fascination," if one has f)nly learned to. note the little 
things, to see and interpret tiic oliscure and hidden things. 
It is surprising what differences there are among school 



42 PEDAGOGICS OF GEOGRAPHY. § 5 

children in this power of observation. The faculty of intense 
and habitual observation does not depend so much upon 
whether pupils are bright or whether they are dull as upon 
their training, though the power to reason and generalize 
correctly from what is observed undoubtedly does depend 
upon superior mental qualities. Among Indians the range 
of inference is narrow, but the keenness of their observations 
and the correctness of their interpretations of signs are well 
known. Much of this acutencss is doubtless inherited, but 
it is perfected by practice. 

Success in life will depend largely on the training that our 
children receive in the art of using their senses. One emi- 
nent authority says that, of two clever boys, the one with the 
-tjuicker perception of things around him is more likely to 
succeed than the other. He adds, however, that the chances 
of the less clever boy will be vastly improved by early, 
judicious, and skilful training. 

Extended argument and insistence are not required to 
make clear and to emphasize the need for training the senses. 
Every parent and every teacher is aware of its importance — 
of the great influence it has in determining one's career in life. 

32. Sensation. — The term sciisa/ioii is of so much 
importance to the teacher, and is in general used so vaguely, 
that an explanation of its meaning seems to be necessary. 
Like many other words, it has a common or conversational, 
and a technical or scientific, use. Its technical sense in 
the science of psychology will be explained in this place. 
The word comes from the Latin word sciitirc, "to feel." 
The human body is so constituted that outward changes of 
various kinds act upon it, and vibrations result that are 
carried along suitable nerves to nerve centers within. No 
one knows exactly what happens at the brain centers where 
these conducting nerves end, but we do know and interpret 
the nerve vibration. These vibrations, from the point where 
they begin to the point where the mind is aware of them, 
is sensation. 

A homclv illustration will make the matter clearer. A 



I 



§ 5 PEDxVGOGICS OF GEOGRAPHY. 43 

spider spreads his net and retires to his cyUndrical hiding 
place, woven at the center, and waits for his expected prey. 
Every radial strand of his web leads to his place of conceal- 
ment. Lying in wait here, sensitive, alert, expectant, he 
typifies the mind. The wind blows over his net and he feels 
the quiver of the silken nerves against which he rests. A 
fly alights upon it. He notes a difference in the vibration — 
the sensation is diiferent. The net can only I'ibratc; it 
cannot feci. When the watcher — the conscious responsive 
center in which the vibration ends and is significant — is 
absent, only a part of the conditions necessary to a completed 
function is realized. The same is true of the body. When 
the tenant of the body — the mind — lies imconscious within 
or is absent, there may still be vibration in response to 
suitable stimulus, but the consciousness of it necessary to 
make that vibration a real and completed sensation, is 
lacking. 

Another illustration is found in the telephone. At some 
distant point a vocal distiu'bance affects a receiving instru- 
ment. Transmitting wires in some mvstericjus way carry 
the impulse along to the place where the person songht is 
usually to be found. He is there, awake, perhaps expectant. 
He hears an alarm. 

Everything that corresponds to a sensation proper is 
included between these two extremes — the disturbance com- 
municated to the transmitting instrument, and the con- 
sciousness of the listener at the other end that there is an 
alarm or a call at the receiving instrument. This strict 
limitation of the meaning of the term sensation is important, 
and should very frequently be useful to the thoughtful and 
intelligent teacher. 

The later investigation concerning what the call at the 
telephone reveals, illustrates a mental operation that begins 
where sensation ciuh. This, called perception, will be 
treated in another paragraph. 

33. Sensations Classiflt'd. — vScnsations are divided into 
three classes, determined by the place where the nerve 



44 PEDAGOGICvS OF GEOGRAPHY. § 5 

vibrations connected with them begin. As has been 
explained, certain stimuli, disturbances, or changes affect 
either the whole body or one of its organs. This disturb- 
ance is carried along the nerves at the rate of about 
200 feet per second, and ends in some brain center suited to 
receive it and to be affected by it. Just what happens in 
these nerves, or what the nature of the tremor or vibration 
at the brain center is, no one knows. We do know, how- 
ever, that in some mysterious way the mind takes notice 
of the change and is capable of interpreting it, just as 
a person is capable of realizing that there is a call at a 
telephone. 

We know, too, quite accurately the place where this 
vibration begins, and it is on this knowledge that the classi- 
fication is made. This threefold division is as follows: 

1. General Sensations. — These are the sensations that 
with respect to their source are either vaguely localized or 
are diiTused over the entire wSystem; as, the sensations of 
zvarnith and eold, of nervous or n\\\&c\\\a.r fat igne, of 7'est and 
motion, of sleepiness or Juinger or thirst. 

2. Organie Sensations.— T\\e organic sensations are those 
that are recognized as belonging to organs situated in the 
visceral and the abdominal regions. 

3. Sensations of the Special Senses. — The most numerous 
and useful of these are the sensations having their origin at 
the eye and the ear. Of less, but of very great importance, 
are the sensations connected with the nose, the tongue, the 
nerves of touch or feeling, and the sense of muscular resist- 
ance, by means of which we are conscious of weight and 
pressure. 

34. Perception, — The derivation of this word does not 
reveal its meaning very distinctly {per, "by means of," 
capere, '"to take"). Its signification can be best explained 
by resuming our former illustration of the telephone. 
vSitting- in my office, I become aware of an alarm or a call at 
the instrument. This, as has been stated, illustrates the end 
of a sensation and the beginning of a pereeption. I am at 



§5 PEDA(;()GlCvS OF GEOGRAPHY. 45 

once conscious of the call; I become aware of it; I begin to 
perceive it. So far, there is no other consciousness than 
that there is a disturbance, a summons. As to what the 
meaning- or purpose of it is, I have no knowledge whatever, 
I g'o to the instrument aud begin an investigation. From 
some point outside the office definite information comes 
along the wire. Item by item this intelligence comes tome, 
until my knowledge of the cause of the call is complete. 
When this point is reached, I hang up the receiving instru- 
ment, ring off the connection, and the matter is ended. 

This illustrates what is meant by perception, except that 
in the case of the real mental operation, there is no such 
break in continuit}^ as the illustration would indicate. When 
there is an alarm or a call in the brain, say from the optic 
nerve, the cause of the nerve vibration — the outside reality — 
is usually known cil o/icc. In other words, the alarm itself 
is caused by the arrival at the brain center of a report of 
certain cjualities in the object of sense outside. Suppose, 
for example, that the external object is an orange. The call 
or alarm is itself a report of the color, size, shape, and other 
qualities of the object. There is no interval between the 
alarm and the investigation that follows. There is nothing 
corresponding to a distinct call that reveals no more than 
that it is a call; nothing to correspond to a leisurely stepping 
to the instrument for the purpose of conducting an investi- 
gation that proceeds step by step in the orderly fashion of a 
conversation. In the case of a sensation the reports of 
color, shape, odor, etc., received from without, come along 
the vibrating nerves and pour into consciousness, united just 
as they are in the external cause itself. A distinct examina- 
tion of each reported quality must be luade before the sen- 
sation has a complete interpretation by the recipient mind 
and is worthy to be called a perception. 

This imion of many nerve vibrations into a simultaneous 
impulse that becomes in the mind a perception of a single 
external reality, is aptly typified by the phenomenon of a 
ray of white light, which is composed of the various colors 
of the solar spectrum. 



40 PEDAGOCilCS OF GEOGRAPHY. §5 

'Si>, Use 3Ia<lo ofl Vi*c'oi)t ions. — 'J'hc foregoing" explana- 
tions of what we mean by the terms sensation -axid^ perception 
are of extreme importance to the teacher. This fact will 
appear more fully in what will be given in later pages. It 
is necessary for iis to consider now the mental use that we 
make of sense perceptions. In doing this, only such of the 
technical terms of psychology as are indispensable will be 
used. 

In order to estimate more exactly the value of these mes- 
sages that come to us from the outer world, let us try to 
imagine the condition of a person with a body divested of all 
nerves of every description. He has eyes with no optic 
nerve, a nose without nerves of smell, and so on for the other 
senses. Inside are the great brain centers, ready to respond 
to vibrations that never come. This great organ of the 
mind, which by its functions enables us to know, to feel, to 
enjoy and reason and hope and fear, is utterly cut off from a 
world outside full of sights and sounds and life and motion. 
Not the slightest knowledge of any kind whatever can by 
any chance come to it. The only evidence that any one 
could get that the body containing such an isolated brain is 
alive would be that it resists decay. In comparison with 
such a being, a man enclosed in an unlighted cavern far 
nnder the earth would be richly endowed with opportunities 
of knowdedge. He could at least feel the shapes of things 
about him and hear the sounds of his own motions. But a 
being of the kind supposed could learn nothing — could make 
no progress of any kind. He would be little more than a 
mass of lifeless matter, like a clod or stone. 

It is clear, therefore, that for all our mental power we 
are indebted to the fact that we are in communication with 
the outside world. Deprived of this, we are practically 
dead. These .sensations that by the vibration of the nerve 
filaments reach the brain, are translated into definite percepts, 
and these are taken into the keeping of nicviory. There 
they are sorted and arranged into classes by the faculties of 
discrimination and comparison. The.se classes are called 
general notions, or concepts. These in turn are fashioned 



§ ') PEDAGOGICS OF CiEOGRAPllV. 4.7 

by the constructive, or elaborative, faculties — fancy, imagina- 
tion, reason — into many other forms, new, curious, wonder- 
ful. So that, having- nothing more to begin with than these 
elementary sensations and perceptions, the mind by its own 
activity becomes the greatest and noblest and most wonder- 
ful thing of which man is capable of conceiving — much more 
wonderful than the world in which it operates. 

36. Iiiii)oi'tanc'e of Attention in Observing". — It 

might be asked why all people are not equally well informed 
about the external world, and why they are so unequally 
intelligent. In answer it maybe admitted that the brain, 
the central organ of intelligence, is finer in some individuals 
than in others. But making due allowance for such differ- 
ences in brain capacity, it might seem that results yielded by 
the senses should be much the same. We all get from the 
outside world the material by which the mind is nourished — 
the sensations, by the interpretation and elaboration of which, 
the mind is strengthened and developed. The human organs 
of sense in a normal condition have very nearly equal 
native efficiency in different individuals, and the sensations 
in different minds vary but little in vividness. If, how- 
ever, any one will notice closely, he will soon discover that 
sensations are extremely complex, and that some of their 
elements are passed over lightly and with little or no 
attention. Look at a rose bush in bloom. "We srr the entire 
mass of flower and foliage, but we )ioticc only the flower, the 
most conspicuous feature. . Even that we see in a vague, 
general way, and the resulting percept is correspondingly 
vague. A botanist stops at that same bush and passes an 
hour or more in a minute and careful examination. He 
turns over the leaves, observes their shapes, their marking.s, 
their margins, their veining, their appendages. We wonder 
what he is doing, and we stop and examine ////// with a some- 
what anxious interest and curiosity. What is he doing ? 
He is translating his sensations into perceptions that as 
exactly as possible represent the complete external reality. 
Ask an ordinary observer to describe the rose, and his 



48 PEDAGOGICS OF GEOGRAPHY. § 5 

knowledge will be nearly all comprehended in the statement, 
" The rose is red." Ask the botanist, and he will tell you a 
hundred things that are new and strange and interesting. 
The one has merely seen roses; the other has observed, 
studied^ and rejleeted about roses. The knowledge of the 
one is fragmentary and miscellaneous; that of the other is 
accurate, organized, and scientific. It is the old story of 
eyes and no eyes. Our percepts, as material for later elab- 
oration by the mind, will gain in value in proportion to the 
degree of attention with which we examine our sensations. 

This method of obtaining the crude or elementary material 
with which the mind works, and without which mental activity 
is impossible, is called sense pereeption. The name is applied 
both to the operation itself and to the percept., or the product 
or result of the operation. The vast fund of percepts, 
which when fully organized into systems is called by the 
various names corresponding to the divisions of physical 
science, is obtained almost entirely by means of the sense of 
sight. Especially is this the case with geography. The 
earth and what is on it — things natural and artificial — 
furnish the subject matter of geography. And it is to the 
eyes more than to all the other senses that we are indebted 
for the percepts representing this great aggregate. Hence, 
it is clear that an indispensable prerequisite to geographical 
study is the early, systematic, and persistent training of the 
senses. If children are to be well and correctly educated, 
this is a matter that must not be left to mere chance. 



37. The Earliest Sensations. — It has been remarked 
that a child begins to observe as soon as it begins to live. It 
is consciously aware of sensations from external objects 
from the very first day of life. The differences between 
these sensations attract attention and furnish the basis of 
such crude classifications as are possible at that early period. 
The sensation from a light is quickly distinguished from that 



§ 5 PEDAGOGICS OF GEOGRAPHY. 49 

caused by a sound; but at first all lights are to a child much 
the same, and sounds are not consciously separated. In 
nearly equal degrees, the moon and a lamp challenge the 
aUention of a very young child, and he is just as likely to 
reach for the one as for the other. The mother's affection- 
ate chirping and cooing are perhaps the first sounds that 
are recognized and vaguely accounted for, and the first wish 
not prompted by mere instinct is for the comforting warmth 
of the bosom on which its young life begins. These are 
the first lessons that relate to the great world. The child 
is getting its first instruction in geography; it is learning 
about the earth and what is on it. The method of. procedure 
is in accordance with an important pedagogical principle. 
The child is beginning with its own environment, and is 
proceeding from the simple to the complex, from the con- 
crete to the abstract. And correct training requires that 
tliis method shall never be departed from during the entire 
period of later education. 

38. The Earliest Sense Perceptions. — At first the child 
is left to himself in the acquirement of those sense perceptions 
that later are to be organized into exact scientific knowledge. 
With tireless persistency he wanders eagerly from object to 
object, seeking fresh impressions. This is his receptive or 
acquisitive period, and curiosity is the impelling motive. 
The mere physical thrill and the conscious mental action 
that accompany the sense perception are in the highest 
degree pleasurable, and they amply reward the physical 
effort that he must make in his search after novelty. The 
higher faculties are as yet scarcely stirred. An edifice of 
scientific knowledge is to be constructed in the future, and 
he is now engaged in gathering the material. As a hetero- 
geneous mass it lies at first in the keeping of the C(;nservative 
faculties; but very soon fancy and imagination will use it in 
erecting many an airy unsubstantial fabric, which they will 
people with all sorts of weird creations of their own. Later, 
this knowledge will all be arranged, and will appear in per- 
manent structures in which shall be seen the scientific 



50 PEDAGOGICS OF GP:OGRAPHY. § 5 

precision and orderly method of comparison, judgment, and 
reason. 

39. Orderly Observation. — It is at this time that intel- 
ligent supervision and direction are most needed by the child. 
The acquisitive faculties are intensely active, but their 
operation is erratic and entirely without choice. As a bee 
in search of honey wanders from flower to flower quite at 
random, so the child wanders, consumed with an intense 
desire only to see, only to hear. There is no logical order, 
sequence, connection, or method in his sensations. Some of 
them are helpful; many of them are hurtful; but, helpful or 
hurtful, good or bad, each makes its impression deep upon 
-the tablet of the mind. The child has little skill in the art 
of observing, and no knowledge whatever of any principle 
of selecting objects. 

If now some one of large knowledge, experience, previ- 
sion, would take the child, and with a view to some ultimate 
end would choose the objects to be observed, determine 
their order of presentation, teach him how to observe them, 
fill out broken secjuences, emphasize indistinct relations; if 
he would gradually introduce cause and consequence, pur- 
pose and result, a great work could soon be accomplished. 
But until at the age of from five to seven or eight years, 
when the child first enters school, no attempt whatever 
is made to systematize this early acquisition of sense percep- 
tions. Even then there is little change from the purely 
incidental and fortuitous method of his observational work 
that was. He is indeed deprived of his liberty to wander at 
will among the sights and sounds of his home environment; 
but, except in a modified way by the kindergarten, no defi- 
nite method is substituted for the delightful freedom that he 
enjoyed. He is taught to read and spell and to deal with 
numbers; but with the relations and magnitudes of concrete 
things as the.'^e relations and magnitudes are measured by 
number, he learns but little; for in his work he u.sually con- 
siders number in the abstract only. This is an entirely new 
experience, and he finds it irksome. The thrill of nerve 



§ 5 PEDAGOGICS OF GEOGRAPHY. 51 

vibration and sense pcreeption that made his earlier con- 
scious life so delightful is gone. Nearly everything that he 
deals with now is separated from the reality. He is trying 
for the first time to use the material already accumulated, 
and the work has in it a repulsive degree of abstractness. 
He is told that c-a-t represents a certain domestic animal, 
but the cunning creature that he remembers so well is com- 
pletely separated from the arbitrary tyrannical symbols. He 
learns that the half of four is two, but there is no confirma- 
tion of the fact by the division with his sister of four tooth- 
some concrete morsels. If he could only illustrate each of 
these abstract propositions by some actual experience, — 
emphasize it by some strong nerve vibration ending in a 
sensitive brain center, — he should remember it always. His 
teacher is trying to reach him by addressing his judgment, 
his faculties of reason, of causation and symmetry and rela- 
tion and order, but they are dormant as yet and refuse to 
respond. 

40. A Critical Stag-e. — Just here is the critical stage 
in the education of a child. If he is handled unskilfully 
now, it will be difficult to overestimate the damage. The 
school authorities in some of our large cities are beginning 
to realize the importance of having the very best possible 
work done during- tlie first year or two of the child's life in 
school, for they are in manv places paying the highest 
primary salaries in the lowest grades. "Let me make the 
ballads of a nation," said Fletcher of vSaltoun, "and I care 
not who makes its laws." For a similar reason the educator 
might say, "Let me direct the early sense perceptions of 
your children, and I care not who educates them afterwards. " 

41. The Greek PedajiTOg-ue. — The teacher of a boy in 
ancient Greece was called i\ pedagogue {jraLdb^ ayioynq, paidos 
agogos, "a boy's leader"). The pedagogue was usually a 
slave, but always an intelligent person. It was his duty to 
accompany his charge wherever he went — to the field, the 
forest, the theater and park and gymnasiiun. He directed 



53 PEDAGOGICvS OF GEOGRAPHY. § 5 

the curiosity of his ward, suggested his inquiries, exphiined 
his difficulties; he helped his inferences and classifications, 
and determined the measure in which the abstract should be 
mingled with the concrete. He accompanied his pupil into 
the midst of the seething democracy of Athens, where might 
be studied the actual doings of the "rulers of men " and the 
ebb and flow of passions in the men that were ruled. Here 
the boy came to understand the rivalries, the ambitions, and 
the general principles and sentiments for which men work 
and struggle, fear and hate, fight, and, if need be, die; here 
he learned of the love of home and country, the pride of 
race, the glory and preeminence of the physical and mental 
and moral excellence that inade his country easily the first 
in the world. From the lips of his teacher the boy learned 
the inspiring beauty and rhythm of his country's poets, the 
w^onderful events of her history, the wisdom of her philos- 
ophers and sages, the elocpience of her orators, and the 
matchless symmetry and perfection of her art. Thus was 
he made worthy to take his father's place in preparing as a 
heritage for after times the spectacle and example of a 
civilization that in many respects has not been surpassed in 
the history of the race. 

How much better all this seems than the course we pursue. 
We shut our children wathin four walls, away from the myriad 
sights and sounds of nature and the busy hum of the world's 
activities, and are surprised and disappointed when they come 
out lacking the virile touch, the educated purpose, and the 
broad views that mean success in the world. 

42. The Parent Slioiild lie tlie Child''s First Teacher. 

Educators are in general pretty Avell agreed that the best 
possible preparation for the study of geography and other 
physical sciences is a careful and systematic study by the 
child of his immediate environment. This should begin 
with general information of every kind that involves the 
.•acquirement of a large stock of definite percepts. Many of 
our schools of late years have courses prescribed in object 
lessons, and textbooks of high merit have been prepared 



§ 5 PEDAGOGICS OF GEOGRAPHY. 53 

indicating- both the matter to be studied and the method to 
be pursued in giving the lessons. But before the point is 
reached where such selected lessons can be taught with 
advantage, the child must be encouraged to observe per- 
sistently, and must be helped to understand the nature, 
meaning, and, to some extent, the relations, of the common 
things about him. This is properly the work of the parents, 
one of the many obligations incident to parenthood. It must 
be done, if at all, before the child passes into the care of the 
salaried teacher. The fact that he is so full of questions 
concerning things that we older people know so well, and 
think that he also ought to know, is conclusive proof that he 
needs direction and help, and that we are the persons from 
whom he should receive them. Instead of being- repressed, 
this tendency of the child to ask questions should be encour- 
aged. If he lags in this respect, the fact should be taken as 
a sign of abnormal and lamentable mental sluggishness that 
should if possible be overcome. If he does not ask questions, 
in the usual manner of children, about the thousands of simple 
things that lie within the range of his daily observation, be 
very sure that he needs the best help you are capable of 
giving him. He is failing to acquire that wealth of elemen- 
tary experience, that supply of sen«e percepts upon which 
all real future progress depends. His entire future mental 
life will very greatly depend upon Avhat he does now. No 
one can help him so effectively as the father and mother, to 
whom he owes his existence; no one can imderstand so well 
as they what he lacks and most needs. 

This work, although the obligation to do it rests equally 
upon both father and mother, is, from the circumstances of 
the case, peculiarly the function of the latter. She is with 
the child constantly. He never passes from imder her imme- 
diate notice without exciting her anxiety and concern. She 
plans his activities and diversions, she coaxes away his little 
troubles, soothes his disappointments, and abates his griefs. 
HoAv much we read and hear of the inestimable influence 
of a good mother. Of men that have taught their name 
to the ages, how many owe what they ha\'e been and done to 



54 PEDAGOGICS OF GEOGRAPHY. § 5 

the affection and intelligence of their mothers. Indeed, the 
believers in heredity and evolution teach that we are more 
likely to inherit or to acquire from early training the best 
qualities of our mothers than those of our fathers. 

43. Etlucational Value of Outdoor Life. — For the 

betterment of sluggish physical health we are advised by 
the medical authorities to exercise much in the open air. 
The advice is equally good for sluggish mental health. 
Some of us fondly imagine that when we carefully retain our 
children within the immediate precincts of home, we are 
keeping them away from the bad influences that lie in wait 
for them outside. Perhaps we are, but it is at the cost of 
having them miss all the wealth of education to be found in 
earth and air and sky. We are depriving them not only of 
the much needed physical activity to be found nowhere so 
well as in the open air, but we are causing them to lose the 
mental and sense activity and the esthetic training that 
find their best nourishment, and are themselves the best 
elements, in outdoor exercise. 

There is a sunburned, rosy-cheeked little fellow of five 
years living in my immediate neighborhood whose mother 
speaks of him half anxiously and half proudly as a "tough 
citizen." He goes everywhere by himself — to the park, to 
the business part of the city, to the woods — where does he 
not go? He inspects all the new buildings that are going 
up, even more closely than do the architects in charge; he 
climbs to the upper floors, exciting the smiles, the anxieties, 
and sometimes the objurgations of the workmen. He 
"hitches behind" passing wagons and sleds; he takes the 
girls, many of them larger than himself, down the hill on 
his sleigh. For blocks around every boy large and small 
knows him, and more surprising still, he knows them and 
their sisters, their fathers and mothers, and can call them by 
name. In summer he is a persistent student of botany and 
entomology, and general zoology. But it is in the subject 
of herpetology, — the science of snakes, frogs, toads, and 
tadpoles, — in which he is most enthusiastic. It is to him a 



§ 5 PEDAGOGICS OF GEOGRAPHY. 55 

source of unending wonder that girls, and grown people too, 
sometimes, are afraid of these wonderful pets of his. At 
the foot of a ledge with a southern exposure he found some 
time ago a colon}^ of ant-lions with their cunning traps for 
catching the ant, which is too busy to suspect a fellow crea- 
ture of a device so guileful and dangerous. The little fellow 
gave me no rest until I consented to go with him to see what 
he called "his funn}^ things." No lecturer was ever so 
flattered by the attention of an audience as I was while I 
explained the situation. He already knew a surprising deal 
about the real lion and his prey, and one could see that he 
quite approved of the name ant-lion. But his surprise was 
unbounded when I showed him the form the creature would 
take when the time came for him to put off the old life and 
take on the new — the nearest physical analogue of immor- 
tality. 

At the cost of some anxiety on the part of the mother, 

some torn clothes and worn shoes, a face and a pair of biisy 

freckled hands often soiled and sometimes torn by protesting 

insidious briers, what an admirable preparation this boy is 

getting for the study of formal geography. And at the 

same time he is beginning the indispensable process of 

induration that ends in the " wrestling thews that throw the 

world." The fear of contamination that shuts so many of 

our boys and girls in the home prison, where w^hite blood 

corpuscles and not red are multiplied iniduly, is largely 

1 aginary. If the boy is strong enough tog-row both mentally 

1 physically under this regime, the bad will not outgrow 

^ pod, the impure the pure. Let him out, and when you 

J 1, go with him. If possible, enter sympathetically into 

h's outdoor life with its diversions and endless wonderment. 

"^h's play and training, under the supervision of intelligent 

nts, is only another form of lessons in physiography. It 

)" b^gin too early, and it brings to the little student 

j'ther satiety nor weariness. 

44. Geo£vi*apliy in Pictures. — If Mohammed refuses 
to go to the mountain, it is often advisable to bring the 



56 PEDAGOGICS OF GEOGRAPHY. g 5 

mountain to Mohammed, The importance of having- our 
children get their notions of things by bringing them 
face to face with the things themselves is pretty evident 
from what has been said in the preceding articles. This, 
however, it is often impossible to do, but it is possible to 
represent most physical things so vividly that the reality is 
no longer an educational necessity. Some one sa3's that the 
best possible definition of a thing is the thing itself, and that 
next in value is a good picture of it. In these days the 
educational value of pictures is becoming more and more 
evident. It is a rare thing to find on any subject a modern 
textbook without pictures; fifty years ago scarcely any illus- 
trations worthy of mention were to be found in textbooks. 
This has been called the age of steel, but with just as much 
propriety it might be named the graphic age — the age of 
pictures. 

45. The Camera In Geography. — ^ The camera is 
bringing to us in ever-increasing profusion exact represen- 
tations of things as they really are in different parts of the 
world. For our concepts of what the earth contains in 
places too remote for us to visit we are no longer compelled 
to depend on the conventional pencil sketch of the drafts- 
man. Cameras that realize the ideal perfection of optical 
mechanism furnish i:s with photographs taken under the 
best possible conditions of light and shade. These are 
reproduced and multiplied by the " new-process " method of 
engraving, and with a faithfulness to the original that is 
equivalent to identity. The wood engraver, with his approxi- 
mations to the truth is gone, and we shall see him no more. 
Just what is in the photograph is shown in its printed 
reproduction. Peary goes to Greenland and brings back many 
hundreds of negative views of its natural features — its flora 
and fauna, its glaciers and ice floes, its inhabitants and their 
homes and surroundings. Our knowledge of what he did 
and suffered during his absence is almost as realistic as his 
own, and to all intents and purposes we have ourselves 
been there. We have seen the desolation of Greenland and 



§ 5 PEDAGOGICS OF GEOGRAPHY. 57 

have crossed its ice caps, but we have escaped its cold and 
the incident fatigue and suffering; and if we should go there 
in fact, it would be difficult to rid ourselves of the impres- 
sion that we had actually vivsited the country at a former 
time. We should meet familiar faces and find ourselves in 
remembered landscapes. 

The physical features of the Philippines and those of our 
late acquisitions in the West Indies will very soon be as 
realistic to us as are those parts of our own country that we 
have not actually seen. The teaching of geography in the 
early future will be very largely a matter of becoming 
familiar with pictui^es, and the geographical conceptions of 
our children will more and more take on a definiteness and a 
truthfulness to reality that their fathers could not attain. 
Indeed, we all of us owe much more than we suspect to 
pictures. For any definiteness in our conceptions of men 
and things we have never seen we are indebted more to pic- 
tures than to anything ehse. Are there among the people we 
know any with whose featui^es Ave are more exactly familiar 
than we are with those of Lincoln, (jrant, Blaine, Conkling, 
Bismarck, or Gladstone? Would it be possible for McKinlev 
or Queen A'ictoria to pass along the streets of any city in the 
world without recognition? Can Lieutenant Hobson ever 
escape being poiiited out as one whose heroism was uniquely 
recognized, and has not the face as well as the name of 
Admiral Dewey been immortalized? 

The voyager that has been around the world, and the 
"globe-trotting" traveler are rapidly becoming common- 
place; and in these days a Homer would not be likely to 
choose as a fit subject for an epic poem the wanderings 
hither and thither within the narrow limits of the Mediter- 
ranean, of Ulysses, the "man of manv turnings." 

46. Concepts I^ei'ived From Pictures. — Except in 
the matter of color, a correct picture of any object is exactly 
like the image formed on the retina when we look directly 
at the object. It is clear, therefore, that in a sense we see 
the reality if we look at its graphic representation. In other 



58 PEDAGOGICS OF GEOGRAPHY. § 5 

words, a picture of anything, as of a landscape, is only the 
image arrested on its way to the eye and fixed upon an 
intermediate surface in such way that it can at any time 
resume its mysterious journey. It can afterwards be studied 
at pleasure even when that which it represents is far away 
or changed or even destroyed. In many ways a picture is 
educationally more valuable than the real scene, for it will 
remain constant, and the impression from it can be repeated 
again and again until the image is indelibly fixed in the 
mind, which is rarely the case with ordinary external objects. 
And besides, there is the greatest exactness and definiteness 
about the concepts derived from a picture, and these come 
from the fact that there is no disturbing motion either in the 
-observer or the thing observed. 

In these and many other ways that will readily occur to 
the thoughtful teacher, pictures have the very highest useful- 
ness in the ediication of children. 

47. IIoAV to Prepare and Use Pictxires in Educa- 
tion. — The writer's attention was first attracted to this sub- 
ject bv noticing the admirable use made of pictures by an 
intelligent mother. She had several small children, and 
remembering, perhaps, the ancient truism, 

Satan finds some mischief still 
For idle hands to do, 

she attempted to find a substitute for the mischief. She had 
a vast fimd of pictures in old magazines, "Aldines, " art 
publications that were nearly worn out, old geographies, 
etc. She procured a large quantity of cardboard ctit into 
several different sizes. Some of the pieces were large 
enough to accommodate the largest pictures, and some were 
for those small "gems" that often cost more time and 
labor than the large views. The pictures were cut out and 
mounted with much care during leisure moments, and in the 
course of time she had a collection comprising many hun- 
dreds, some of them works of high art. They were regarded 
as treasures worth}' of being cared for; they were not scat- 
tered about the house at random or ruined by rough usage : 



§ 5 PEDAGOGICvS OF GEOGRAPHY. 59 

they were kept in a suitable receptacle. When they were 
used the mother presided, and I have myself sometimes 
accompanied those children in their imaginary voyages to all 
parts of the world. Nothing delighted them quite so much 
as to have their niother personalize the pictures — tell thern a 
story of which the pictures furnished the visual facts or hinted 
at them. Fortunately, this mother was gifted with imagina- 
tion and fancy, the "vision faculties," and her stories were 
some of them so charming that we "older children" were 
usually compelled to listen to them. There was scarcely an 
animal known to man that was not depicted in her collecti(jn ; 
and even the fabulous creatures of mythology were all there. 

48. Value of Pictures in Acciuirijig- a Voctibulary. 

It was frequently possible to hear the children referred to 
above telling the stories of those pictures to one another or 
to some childish visitor. In doing so, there was an obvious 
attempt to reproduce the language employed by their 
mother, and with the aid of the pictures they often suc- 
ceeded in doing so to a degree that was surprising. Another 
thing that was very noticeable was their easy familiarity 
and confidence in using the hard naines that some animals 
and other objects are called. Some one says that when the 
objects represented are equally well known, one name is no 
harder to a child than another; t\r<\.t Iiif>popot a i/iiis is no more 
difficult than horse, provided the animals denoted are dis- 
tinctly conceived. I shall never forget the astonishment of 
a lady caller that took a little three-year-old on her lap and 
began to question him about the pictures. 

' ' What's that ? " "A lion. " 

' ' And what is that ? " "A tiger. " 

" Well, you can't tell me what that is." "A giraffe. ' 

" Goodness! What a bright boy ! What's that ? " 

"A hippopotamus. " 

" Dear me! Who would have believed it ? Well, what's 
that?" 

"A basilisk." 

And so the catechizing proceeded until the visitor was 



60 PEDAGOGICS OF GEOGRAPHY. § 5 

convinced that she had found a boy of extraordinary pre- 
cocity. 

There is little doubt of the correctness of the theory that 
a given word is utterly useless to a person until he knows 
the concept represented by the word. When he has this, 
the word becomes inseparably associated with it. And it is 
equally clear that coherent, discriminating, and comprehen- 
sive thought activity requires a large store of sharply 
defined and vivid concepts and a correspondingly large store 
of words. Hence, the educational value of any means of 
rapidly accumulating a large stock of words, of which the 
sense is distinctly and accurately represented by concepts, is 
very obvious. And of the various methods of increasing a 
-child's vociibulary, there is perhaps none that will yield 
better results than the method with pictures. Every teacher 
of geography should begin, at the very outset of his prepara- 
tion for the work, to accumulate a collection of these impor- 
tant helps. They will be found i;seful in many other ways. 
It would be difficult to find a more suggestive and helpful 
subject for a composition than a good picture, and for off- 
hand oral description they are unequaled. Every one kno\A's 
the importance of a good vocabulary, but not even every 
teacher fully realizes what a valuable fimd of concepts and 
the words that denote them may be obtained from a collection 
of good pictures. 



cot^i.eictio:n^s ix naturat. scie:n^ce. 

41). IN'atiiral Science in TjONver School Grades. 

During the last twenty years the subject of object lessons in 
the public schools has developed very decidedly in the direc- 
tion of natural science. The work has not been well 
organized, however, nor have its exact place and time in the 
school curriculum been generally agreed upon and fixed; 
yet the fact that oral teaching in elementary science has 
been undertaken in many of the best schools of the country 
indicates a wide recognition of its usefulness and importance. 
Many attempts have been made to furnish textbooks that 



§ 5 PEDAGOGICS OF GEOGRAPHY. Gl 

would enable the teacher to proceed with the work in a 
manner both orderly and intellii^ent ; but a difficulty that at 
present seems msuperable is found in a general want among- 
teachers of an acquaintance with the various elementary 
sciences. It is evident, however, that the present tendency 
is strongly in the direction of natural science; for the won- 
derful advancement that marked the closing years of the 
nineteenth century was owing almost entirely to man's 
increasing mastery of nature. And there is not the slightest 
likelihood that this utilitarian development of science will 
have a pause; so that knowledge of these subjects and of the 
best methods and appliances to be employed in teaching 
them will soon become imperative upon every teacher. The 
teacher must in the early future be thoroughly familiar 
with the general principles of science, and it is, these 
demands that come with advancing civilization, and that 
cannot be ignored, that are making a real — a learned — pro- 
fession of teaching. 

50. ^Tatural Science in Relation to Geography. — In 

earlier parts of this work it is clearly shown that every 
science is correlated with geography — that geography is, so 
to speak, the "mother lode" of all science. But in the gen- 
eral subject of olyect lessons, which is almost exclusively 
scientific, there are only certain phases of it that bear 
directly iipon geographical teaching. Of these, botany, 
zoology, geology, and mineralogy are the bost examples. 
Object teaching did not at first include these sciences, but 
one by one the natural .sciences have most of them made 
places for themselves in the oral concrete work of the 
schools. Of course only very elementary lessons, always 
illustrated by prepared specimens, or given among- the 
objects as they occur in the broad field of nature, should be 
attempted. It would be difficult to find a better method of 
giving reality to the work of geography proper than we have 
in expert object teaching. Provided each lesson is properly 
illustrated by specimens, the work can be made of the most 
intense and absorbino- interest. 



G2 PEDAGOGICS OF GEOGRAPHY. §5 

Since so few teachers know what to collect and how, no 
excuse need be made here for introducing' a somewhat 
detailed treatment of the subject. 

51, Botanical Helps. — Man is largely indebted to the 
vegetable kingdom for his food and his clothing, and for the 
shelter of home. " What do these people eat ? whence does 
it come ? and the material of their clothes, what is that ? " 
These are questions of geography, and the answers to them 
will be fully intelligible only when the pupil has the prelim- 
inary preparation necessary to understand them. It is 
important to know more about coffee than that it is the seed 
of a certain shrub; that tea is the dried leaf of a bush; that 
cotton, linen, hemp, and jute are vegetable fiber. The child 
should, if possible, be enabled to conceive of these things as 
they are in their native environment. To do this properly 
is less difficult than is generally supposed. Nearly every 
natural object illustrates something in science; and, when 
closely examined, becomes of absorbing interest and rich in 
instruction. Such objects are about us on every hand, and 
if they are not, they are usually easy to obtain. Most 
abundant and accessible of all are botanical specimens, 
which, when properly mounted, become objects of beauty. 
Did you ever examine, with eyes open to the beautiful and 
the various, a collection of woods, of seeds, of vegetable 
tissue, or- an album of ferns, of mosses, of lichens, or of sea- 
weeds ? If you have not, you are not aware of the vast 
resoinxes for diversion and instruction, of the opportunities 
of studying the signs of intelligent purpose and the adapta- 
tion of means to ends, that are escaping you. 

Every teacher of children should have a large botanical 
collection that he himself has collected. It should be a 
collection that constantly increases in size and scope, one 
that he has studied and continues to study thoroughly. For 
collecting, mounting, and preserving such a collection, almost 
any standard work on botany will give him minute instruc- 
tions. As his herbarium grows in size, he will wish to 
arrange his specimens in accordance with their scientific 



§5 PEi)A(;()(Ucs OF CxE()(;raimiv. g;3 

subdivisions; and as tliis work progresses, he will find how 
very many desirable specimens he lacks, and his eagerness 
to obtain them will increase in proportion as his desires are 
satisfied. I suspect that, if a botanist could get a specimen 
of every vegetable organism, he would, like Alexander, weep 
because there is only one world to conquer. 

53. The National Museiiiii. — Comparatively few per- 
sons know of the Avonderful work in science that is going on 
at Washington. The National Museum has many collectors 
in every part of the country and the world; and what it has 
accumulated, classified, arranged, and is caring for, surpasses 
belief. Every department of art, science, and industry is 
illustrated in that wonderful collection. Moreover, the hearty 
and W'illing helpfulness shown to any inquirer by- the corps 
of scientific men in charge would almost convert on6 to a 
belief in altruism. I find a natural object of any kind that 
I cannot identify; they will instruct me at the mere asking. 
I need the best and latest literature on any given scientific 
subject; they will make it accessible to me in the easiest and 
cheapest way possible. They are always ready to exchange 
duplicate specimens with me on terms that seem always 
highly advantageous to me. Every teacher should be in 
close touch \vith this beneficent institution, not, how^ever, for 
the purpose of being helped only, but with a willingness and 
a pride in being a helper and a contributoi*. 

Mann's " Catalogue," which can be obtained at "Washing- 
ton, contains the post-office addresses of botanists in ever}^ 
part of the country, who are willing to exchange specimens; 
and, besides giving a numbered list of all the plants of the 
country that are known to .science, it contains much other 
information useful to the botanist. " Check-list.s, " giving 
the names, localities, chemical composition, etc. of all cata- 
logued objects in every department of science, may be 
obtained from the gentleman in charge at the National 
Museum. 

As has been said above, it is not the object of this paper to 
instruct the student in the details of making a herbarium or 



G4 PEDAGOGICS OF GEOGRAPHY. § 5 

other collection, but to emphasize the importance of havin<^ 
such a collection as a help in the study of geography. 

53. Serial Specimens. — Many of the plants that have 
value in commerce, even if they were of easy access, cannot 
be included in the teacher's collection. Some of them are 
large trees; as, the date, the banana, the breadfruit, the 
orange; others are succulent and perishable; as, the pine- 
apple, the mango, and most edible fruits. These can be 
illustrated by pictures showing the plant in different stages, 
and the history of the commercial product on its way to 
market. Take, for example, the story of cotton, from its 
place of growth in the fields of the South, to the finished 
fabric issuing from the mills in the North. A full series of 
lessons on this subject can be made almost as • rich in 
geographical concepts as actual travel, and the incidental 
cominercial and industrial information is important and ver}' 
valuable educationally, besides being of extreine interest. 
These specimens of every kind, when arranged serially, 
furnish the best possible guide in giving the lessons. Of 
course the teacher must go to considerable trouble, and some 
little expense, perhaps, in informing himself thoroughly, 
and in procuring specimens, pictures, descriptions, etc. 

The following outline will indicate the general plan of such 
a course of lessons and the illustrative material required: 

1. Cotton. — Its three principal varieties — specimens of 
each. Call attention to the long silky fiber of the sea-islmid 
variety, and compare with the others. 

2. Its Relatives. — It belongs to the iiialhno family, and 
is therefore a relative of our common mallows, the hollyhock, 
the Indian mallow, the hibiscus, the althea ("rose of 
Sharon "), the marshmallow, etc. Show specimens of these 
blooins, and coinpare with the bloom of the cotton. (Cotton 
can be bloomed easily in any part of the United States, but 
the boll will come to perfection only in the South.) 

3. Its Habitat and Cultivation. — Show habitat on 
maps — pictures of cotton plantations — hoeing — picking. 



§0 pei)AGu(;k;vS OF (;e()graphy. hj 

Give some account of the people engaged in this work — the 
negroes, their homes, amusements, songs, etc. 

4. Preparing- for Market. — Picking, ginning, baling, 
shipping, etc. The cotton gin, sketch of Eli Whitney, etc. 
Many pictures can be found to illustrate this topic. 

5. Manufacture. — The water-power of the rivers of the 
Atlantic slope in New England — "The mills on the Merri- 
mac" — spinning-jenny, loom, etc. Manufacturing cities, 
with explanations why they are so. 

These materials relating to particular topics should not be 
allowed to fall into confusion, for in such case they become 
mere iinpcdimoita without any value whatever. The teacher 
should ba constantly on the alert to improve them by addi- 
tions, and should keep them in large envelopes properly 
labeled, or in any other suitable receptacle. Seeds of various 
kinds kept in small bottles or in boxes of uniform size, 
labeled, and arranged in cabinets, make collections of miich 
u.se in the classroom. Many of these can be arranged in 
series, and may be used in connection with mounted botan- 
ical specimens or with pictures and drawings. 

When properly prepared, the varieties of useful woods make 
a very pretty collection. If the teacher can afford it, or if 
he can induce his school authorities to bear the expense, the 
various woods of the country can be bought prepared in the 
best possible fashion for educational purposes. Very thin 
sections cut across the grain, with the grain, and radially are 
beautifully mounted, fully labeled, and arranged in bound 
volumes. These are not for decorative purposes merely; — - 
beautiful adjuncts to the parlor and librar}- — they are in 
the best sense educational, and are of especial value to the 
teacher of geography. Every person should know the varie- 
ties of the useful woods. 

A note of inquiry to any large book concern will obtain 
for a teacher all the information needed to procure this 
collection. 

54-. Other Collections. — A well equipped school build- 
ing should be a museum on a small scale. The ofreat wide 



GO PEDAGOGICS OF GEOGRAPHY. § 5 

world outside should be represented there by collections of 
many kinds, and these should be cared for and systematically 
used. For the young, as yet unable to make much use of 
mere abstractions, they are better than textbooks. Speci- 
mens illustrating- the rock for Jitat ions shovdd be there: 
granite in its many varieties, trap, calcite, trachyte, mica, 
syenite, the protean forms of quartz, and any others that 
will set pupils to observing; for, unless the teacher is him- 
self an observer and is able to develop the same instinct in 
his pupils, his work in the field of nature at least will be in a 
large sense a failure. 

A small collection of the ores of metals having industrial 
value, and of other minerals useful to man, will add much to 
the interest pupils take in geography. For example, in the 
case of coal, if the teacher can exhibit to a class all the vari- 
eties in the series, beginning with peat and lignite and end- 
ing with anthracite, it will add much to the geography of the 
subject. Seeing a collection of the butterflies of Brazil, a 
pupil at once imagines them as one more feature of reality 
in his conception of the vast woods along the Amazon. 

The writer once received from a friend some of those 
beautiful flowers — the edehveiss (" noble-white ") — that grow 
in the Alps. They were to him not daint}^ white flowers 
merely, to be prized for their beauty and strangeness, but 
they served in a way to bring those European mountains 
into immediate touch with his own personality — they became, 
as it were, a symbol or representation of the mountains them- 
selves. Nor is this mere sentiment. Underlying it is the 
psychological law of association. Nothing not known directly 
by means of the senses can be satisfactorily conceived except 
through many and various associations. These are the links 
that bring it into connection with consciousness, the marks 
that distinguish it from other things. 

Not immediately connected with geography, but often 
giving interest and reality to some of its most important 
facts, are many other objects suitable for use in school collec- 
tions. Among these are animal forms that may be pre- 
served in small space; such as specimens illustrating the 



§ 5 PEDAGOGlCvS OF GEOGRAPHY. 07 

important genera of insects, insects that are injurious to the 
interests of man, and the enemies of these pests, together 
with many other collections of high educational value. 

55. Difficulties. — Many and serious difficulties await 
him that would be a successful teacher of science in any of 
its departments, but all of them may be overcome if he is 
willing to pay the usual price of success — labor, persistent 
labor, with a well defined, clearly perceived object. Of one 
thing he may be assured; it is, that in the future the suc- 
cessful teacher of science will place less reliance on text- 
books, and will depend more and more on concrete material, 
which is the substructure of all science. With increasing 
skill the teacher of the future will learn to direct his pupils 
in original research. To do this, he must himself be an 
experimenter, an investigator among the realities and prin- 
ciples of nature. This is a textbook that never gets old and 
out of date, but is always full of inspiring newness and fresh- 
ness, and rich in the suggestion of new discoveries. 

56. 8ii' Arcliibald CJeikie's Reniai-ks. — In concluding 
this important phase of the subject, perhaps nothing more 
weighty could be given than the following words of Eng- 
land's Director-General of Geological Survey, Sir Archibald 
Geikie. vSpeaking of geography, he says: 

The teacher that would gain the greatest amount of personal enjoy- 
ment from the cultivation of this subject, and would most successfully 
use it as a discipline in tlie education of others, should, as far as he 
can, make himself acquainted with the practical pursuit of at least one 
department of natural knowledge. The man that has once dissected 
a plant and has practically studied the mutual relations and functions 
of its several parts, or has himself traced the connection between the 
topography of a district and the nature of its underlying rocks, has 
acquired an experience that gives to his teaching of these subjects a 
precision and vividness that could never be gained from books. And 
in proportion as he cultivates the spirit and habit of personal observa- 
tion and inquiry will his labors among the young be satisfactory to 
himself. • I do not, of course, mean to imply that good geographical 
instruction is nnpossible without scientific acquirement on the part of 
the instructor. But I insist that as geography, though it may not 



c.s i'i':i)A(;()(;irs ( )!■ ci-.ockAriiN'. §5 

(.'laiin to he itself ;i ilistiiiel seiiMiei,', is l);is(.'(l iipDii and wea\TS together 
tlie work of iiuuu' seieiiees, its lull value as an instiuineut ot" ccUieation 
eamiot be obtained exeejjl by llii>se that are imbued with the scienlilie 
s|)irit. *****-x- 

TIk.' teaehei' uiusl be eontcnt, i)atit'ntl\' and thorou,t;hly, lo master his 
siibjeet. JIc should bcj^in by diveslinj;' himself ol' the ct)mmou notion 
that the teiieliinj;' of geography can be taken up by anybody at pleasure. 
When he has realized what geography in the true sense is, he will 
reeognize that to make satisfaetory use of it for ])urposes of instruetion 
demands (lualilieations of no mean or ordinary kind. lie will see that 
a wide range of reading is absolutely neeessary to him, and that he 
must e(pii]) himself with sueli a store of illustrations gathered from all 
dej)artmenls of knowledge as will (.'uabk' him to elueidate eaeh sul)jeet 
as it arises. 

'This is the ideal of geographieal teaehing, and until some approach to 
it is reached I cannot believe that geography will take the place that it 
is entitled to hold in our educational s\'stem. 



GEOCillArJI^ WI IIIDUr A TEXI 15()()K. 



M>L\vSITRF,S A^iy TIIKIU APl'LK ATIOIS^S. 

57. An lOarly IJ(Miiiii'<>m<.Mit . — In the elTort to extend 
the child's view beyond his immediate siirroiniding"s, the first 
need is for an exact conception of certain common nnits of 
nieasiire. 'Phis is a matter of i)rime importance, for, in the 
al)sence of siicli knowledo^c, inteUigent proo-ress is impos- 
sible. Cliief amono- these are the commonly used units of 
leng-th and stirface, without whicli the cliild is certain to find 
the languas^-e of s^-eot^-raphy nearly meaninoless. Unless he 
])ossesses well defined concepts of the linear units he will be 
utlcrU' unable to oei beyond the environment of home, and 
with(jut a knowlediic of the surface units — especially the 
scpiare mile — all cotmtrics will be of practically the samesi^c, 
antl in comparison, each is only vajafuely lar(>'er than his 
father's farm or the stirface l)oimded by his visible horizon. 
More and more witlcly to know the snrface of the o-reat earth, 
tmtil at last he can take into his mind as a conscious reality 
the conce])tion rcprescntino' the scientific dcscrii)tion, "The 



§5 ri<:i)A(;()(;iCvS ()1m;i<:()(;kaimi \'. c'.i 

carlli is ;i j^rciit liall swiiii^iii,^' in space " — lliis is an indispen- 
sable condition to a j)i"oper kno\vlcdi;"e of s^eoj^ra])!!)'. 

With the shorter of these nnits — the incli, tlie foot, and the 
yard — the youni^" student (juickly j^-ains a fair dcj^rce of 
familiaritx' ; but it is coniparali\-cl y bite in liis school course 
when lie i4ets to know with any deiinitencss the rod and llic 
mile. If he could actually travel, — not on llic i-ailway Irain, 
behind whose speed the features of tlie landscape vanish like 
those of a di'cani, but in the manner of oui- anccsloi's, on 
foot, on horse])ack, or in Ihc slow, lunibci-in^' wai^on, he 
mi_!4'ht (piii'kb' .L;ain a notion, ciupliasi/.cd and \i\iricd by 
muscular effort and fatij^'ue, of what is meant by a mile. 
But U) obtain conce])ts of these lont^-er measures of len^lh by 
the e.\penditui"e of pci'Sonal ph\-sical force, is a form of 
practical teachin;..^- that is denied to most of our childien. 

Tt is clear, then, that children recpiire systematic instruction 
in units of length, and that this insti'uctiou should bci^in 
earlw Most people ima_u;'ine their knowlcdt^e of these units 
to be \'cr\' precise, but the\' ai'c in error. Ask tin; ])cop]e 
you meet on a counti"\' road how far it is to the ne.xt villa^v. 
"Oh, about a mile." ^^)U j^o on for a mile and ask ai^'ain. 
*' Well, it's about two miles." Ask \-our pupils to ,^o one b_\' 
one to the blackboai'd and tlraw withont measui"cnient a line 
one foot lon^i:;' or one yard lon^'. iMcasure these lines after- 
wards, and you will be convinced of the need for this kind of 
teachinj^-. 'I'he measures of the I'rcnch mcti'ic system are 
no more vaj4'ue to the average American adult than are oui" 
common l^^nt^'lish measures to the children in our schools. 
'I'hcy would (k'tect no improbability in a statt-'Uient that some 
one acconi])lished a distance of t\vent)'-fi\'e miles in a walk 
of two hours before breakfast, and they would nex'cr think 
of ([Uestionin_<4- a statement that some athlete thi\'W a twelve- 
pound sledj^'e si.xty-onc rods, or jumped over a bar two and 
one-half rods hi<4-h. Try it with your pui^ils if you can do so 
withotit showini^' by your face the absurdity of the ni^ures. 

58, ]M(>tlM>(l <>(■ l*ro<M><l II re. TCverv school should be 
am])ly ])ro\-ided with measures (jf ex'ei')' kind. lla\'ini.;' these, 



70 PEDAGOGICvS OF GEOGRAPHY. § 5 

the teacher should begin with the inch, and require the 
pupils actually to measure everything about the classroom. 
" How long- is your slate; how wide ? " " Find the length, 
the width, and the height of your desk." The dimensions 
of the panes in the windows, of the panels and stiles of the 
doors, and of books, papers, and magazines may also be 
found. Sufficient exercise in actually measuring various 
objects should be followed by practice in giving lengths 
either from memory or by estimate, and this should then be 
combined with exercises with feet and yards. The objects 
should be to educate the eye to accuracy, and to establish in 
the mind the exact relations between the inch and the foot, 
and between the foot and the yard. 

Very interesting and profitable exercises may be had in 
cutting or marking ribbon paper or any other cheap linear 
material. Require the pupils to mark or cut off prescribed 
lengths; as, 5 inches, 1 foot 3 inches, etc., and then to ascer- 
tain by actual measurement how near was their approach to 
the truth. By ascertaining the per cent, of accuracy attained 
by each, some curious and valuable information concerning 
differences in individual aptitudes may be obtained. It is 
well known that, among men engaged in certain trades, 
there are always a few that can judge lengths and sizes with 
a very great exactness by means of the eye alone. Some 
machinists and blacksmiths will select without measurement 
any required size of iron in rod or bar; or one carpenter will 
give correctly the dimensions of lumber, windows, doors, 
panels, floors, and buildings with wonderful precision, while 
another must rely upon actual measurement. These same 
differences may be discovered among the pupils in a class- 
room. The advocates of the theories of heredity find an argu- 
ment in the fact that in estimating dimensions the eyes of 
boys in general are more susceptible to training and are 
more accurate than those of girls. 

In these and similar exercises should consist the beginnings 
of geographical teaching, and if thej^ are omitted or done 
poorly, the error will aiTect imfavorably all subsequent work 
in geography. 



§ 5 PEDAGOGICS OF GEOGRAPHY. 71 

59. Units of Greater Leiig-tli. — Of course the inch, 
the foot, the yard, and even the rod are of Httle use in giving 
definiteness to the conception of distances and dimensions in 
geography. These units are employed in ineasuring the 
things that make up our immediate surroundings. But in 
order to conceive, a mile clearly, we must be thoroughly 
familiar with these shorter units. Each one of them is in 
turn the best help to an exact knowledge of the next higher 
unit. To conceive a rod directly, and without referencj to 
the number of feet or yards that compose it, is more diihcult 
than to think of it as being equal to 5|- yards or 1G|- feet, b::t 
it is by no means easy to get directly a mental picture of a 
mile. Within the limits of distinct vision, objects of an inch, 
a foot, or even a yard in length are fully and sharply repre- 
sented in the picture on the retina, and at the same distance, 
a slight angular sweep of the eye will take in and measure a 
rod. With a mile, however, this cannot be done. Unless 
tlae observer is at a distance too great for distinct vision, this 
useful geographical unit cannot be included in the retinal 
image. Under the conditions of ordinary experience much 
tiras is required to get a clear idea of a mile. The teacher 
that can give such an idea to his class must be skilful indeed. 
In the prairie country of the Far West the task is easier, for 
there the unit of farm land is a square one mile each way, 
and Western children quickly and accurately obtain the idea 
of a mile. Having this, the children in Kansas, for example, 
a state 400 miles long and 200 miles wide, have little diffi- 
culty in making a very definite mental picture of their own 
political domain. Provided a pupil has obtained a clear con- 
ception of such a unit of measure as the area of Kansas, about 
80,000 square miles, how much niore significant become such 
facts as that the square miles in the area of Cuba are nearly 
42,000; of the Philippines, 143,000; of Japan, 148,000; of 
Great Britain and Ireland, 120,000, etc. 

60. Units of Surface. — The square mile is the surface 
unit of geography. Without some superficial measuring 
unit, no clear notion of such instructive comparative areas. 



72 PP:DAG()G1CS OF GEOGRAPHY. §5 

as are mentioned in the preeeding paragraph, is x)ossible. 
No inquiry with respect to any country is tiiore natural than, 
" How large is it?" " How does it compare in area with 
Pennsylvania, my own state ?" France, for example, is two 
and one-half times as large as Kansas; that is, its area is a 
little more than 200,000 square miles. Now, if the pupil 
knows from actual observation and experience what a scpiare 
mile is, he has only two steps from his simplest unit to the 
great area he wishes to measure: square mile, Kansas, 
France, just as soon, therefore, as he has been taught to 
take the full definite ilea of a square mile into his mind, he 
should be furnished, with some convenient larger unit, such 
as the one mentioned above — the area of Kansas. 

This latter part of the work, however, belongs in the later 
development of the subject. The earlier exercises with sur- 
face measurement should be very simple. When a child has 
mastered the simplest linear iinits, he is prepared for those 
delightful manual employments that are becoming more and 
more common in our schools — drawing and paper cutting. 
Every school should he provided with a full set for each 
pupil, of rulers, lead pencils, and scissors. Require the 
pupils to rule their slates accurately in square inches, to 
rule paper and cut it into scpiare inches, and to cut out in 
one piece G, 9, 12, 18, etc. square inches. Have them divide 
the blackboard into square feet, make a drawing of it, and 
divide this so as to represent square feet. Measure the floor 
also, and make a drawing of it in which one-half inch in the 
drawing represents a foot in the dimensions of the floor. 
The teacher owns a tape line; let him cause the school build- 
ing and the surrounding yard to be represented to scale in a 
drawing. Have the drawing of the building placed where 
it belongs. Delegate a committee to measure the distance 
from the school gate to certain well known points. Let the 
teacher represent these points properly on a large sheet of 
manila paper, and fill in other details tmtil he has a map of 
the block, the village, the township. After this he is prepared 
to make in the same way a map of the county, but, of course, 
without actual measurement. And so this observation, 



§ ,-) pedagcxtICvS of geography. r;5 

accompanied l)y representation of Avhat is observed, i^'ocs on, 
and all the time there will be an increasing definiteness in the 
geographical concepts of the children, and a preparation of 
mind that will make the subseqnent study of geography 
seem "a delightful study of a real round world," Sooner 
or later, too, the pupils will know what is meant by a square 
mile. 

No attempt is made here to indicate the gradation of these 
exercises with respect to difficulty, for it is assumed that each 
teacher will do that best for himself. The principal point 
insisted on here is that this work should be begun early, 
and should be continued systematically until geography has 
become a thing of attained reality to the pupil. 

Gl. Anj>'iilai' Measiirenieiit. — .Vny point in a plane is 
located with matliematical precision when just two things 
are known — its direct io)i and its distance from a fixed point. 
In a similar way, every place upon the earth is located by 
giving its distanjc north or soutli of the ecjuator and its dis- 
tance east or west of a selected ncjrth and south line. But 
since the eartli is not a plane but a spliere, these distances 
should be given, not in linear, but in a.igular imits — not in 
miles, but in degrees, minutes, and seconds. 

Manifestly, then, early in the work preparatory to geo- 
graphical study, the circle should be introduced: the terms 
necessary in talking about it, — diameter, radius, circiiiiifer- 
ence, arc, <i>igii-\ — should be made perfectly familiar to the 
student. 

The subject of angles should be taught very fully and care- 
fully. Show first the right angle,— the "square corner," — 
and that this is the same for every circle whether large or 
small — it is always a square corner. So develop the fact 
that a given angle may have arcs of every length, according 
to the size of the circle. Gradually get to the measuring 
unit of ang-les, the degree. Teach the pupils both to under- 
stand and use such expressions as "an angle of 1°," "an arc 
of 1°," " an angle of In''," "an are of 15'"," etc. 

During this early instruction, nothing, or very little, 



74 



PEDAGOGICS OF GEOGRAPHY. 



should be said about minutes and seconds; the important 
objects to be reached are definite ideas of angles and arcs, 
especially an angle of 1" and an arc of 1°. Besides, it should 
be thoroughly taught that every circle is divided into 360 
equal angular parts called degrees, and that the arcs corre- 
spond to arcs varying in length according to the size of the 
divided circles. In doing this, much use must be made of 
drawing, both by the teacher and the pupils; for the subject 
is more difficult than the young teacher would suppose. It 
is a matter that should be persisted in with a careful avoid- 
ance of difficulties that might discourage the pupil in the 
early stages of his work. 

02. The Protractor. — One of the most helpful instru- 
ments in the study of angular measurement is the protractor 
(Fig. 1). Even quite young pupils can be taught to use it, 




and very quickly to imderstand its usefulness. These may 
be obtained at a stationer's, or, better still, they may be 
made from bristol board by the pupils themselves. For the 
earliest work a graduation dividing the semicircle at inter- 
vals of 5° is- all that is required. A protractor of the size 
shown above will be quite large enough for all ordinary 
classroom use. Very many and interesting exercises in 
measuring and constructing angles and arcs maybe had with 



§ 5 PEDAGOGICS (3F GEOGRAPHY. 75 

protractors, and in this way the pupil will quickly become 
familiar with the important and useful circular measure. 

In connection with the protractor a pair of dividers, or, as 
they are usually called, compasses, are indispensable. The 
knowledge obtainable by their use is all in the industrial 
direction, and in this practical age it would be diiificult to 
mention a stronger reason for learning early to use such 
implements. 

63. Measuring" and Constructing" Ang-les. — This is 
an exercise of such general practical utility that it should be 
introduced quite early into our schools. The fact is, how- 
ever, that it is almost entirely igncjrcd, and although the 
subject of circular measure as given in our arithmetics is 
studied by our pupils, it is never in the slightest degree 
understood by them unless they are fortunate enough to fall 
into the hands of a teacher sufficiently intelligent to realize 
its importance. If the pupils are provided with a protractor, 
a pair of dividers, a ruler, and a pencil, tlicy have all the 
implements needed for practice of the most valuable kind. 
The close connection of the subject with geographical place, 
time, and distance; with latitude and longitude; and with 
the changes of season, is the writer's excuse for emphasizing 
the matter in this place. While the most important appli- 
cations of the subject belong in the later stages of geograph- 
ical study, the beginning of its development should be with 
the primary pupil. B}^ the time a pupil is familiar with 
denominate numbers, he should be perfectly acquainted with 
angular measurement, and should be able to estimate an 
angle of G0°, 45°, 30°, etc. as closely as he can estimate 
inches, feet, or yards. He should be quick and accurate in 
measuring angles, and in constructing angles of a given num- 
ber of degrees. 

64. The Mariner^'s Compass. — Among the various 
matters of general information having special reference to 
the subsequent study of geography is that of the luar'mer' s 
compass. This is exactly represented in the engineer's 



70 PEDAGOGICvS OF GP:OGRAPHY. § 5 

compass and in the ordinary pocket compass now very easily 
obtainable. If the teacher will obtain a thin piece of steel,' 
have it tempered very hard, and then magnetized to satura- 
tion at a d3mamo in some electric plant, he can make it serve 
as an excellent substitute for a compass. It needs only to be 
suspended by nueans of a string without torsion, so that it 
will remain in a horizontal position. Every child in the 
classroom should be able to point very exactly and without 
hesitation in any required direction. The pupils should be 
familiar not only with the four principal directions, but also 
with the principal intermediate directions; as, northeast, 
southeast, etc. 

I was very much surprised to find that in the Far West 
directions and distances are given very exactly even by 
young children. "You must go two miles north and one 
mile west," they will tell you. This arises from the plan of 
the government survey, but there is no reason wh}- the 
children in the East should not be trained in this respect. 
They are not, however, for even well advanced pupils are 
ignorant of these matters, many of them not knowing with 
any certainty the places of sunrise and sunset in their own 
horizon. One of the most intelligent men in this city, who 
was born here, in giving the direction of north to an inquirer 
recently, was just about 45° astray. 

Such information is of the highest practical value, but it is 
not taught with any system or persistence. Very certain is 
it that no one can undertake and make a success of the study 
of geography if he is ignorant of these important preliminary 
matters. It is a work that should be planned by the teacher 
in minute detail and carefully adapted in difficulty to the 
capacity of his pupils. 

In teaching direction, it is a good plan to have pupils first 
ascertain from a map the situation of one place with respect 
to another, and then indicate the air-line direction by actually 
pointing. Thus, ask the pupils to ascertain frcnn their map 
the direction from their home to Philadelphia, New York, 
Washington, Pittsburg, Montreal, and then require them to 
point with approximate correctness towards these places. 



§ 



pEi)A(i()(;ics OF gi<:()(;rai'1iv. 



(i5. Mercjitor's l»r<).j<,'cli<>n. — .Vlthoiigii the ciirth is 
nearly spherical., the impossibility of showiiiL^" its entire 
surface at one view has led the chartographers to represent 
it as "round like a cylinder" instead of " roiuid like a ball " 
(Fig. 2). Under this assum])tion, its surface, if we imagine 




Fig. ~>. 



it removed as indicated in the figure and spread out on a flat 
surface, is a rectangle. The objection against thus repre- 
senting tlie earth's surface is that the parts near the poles 
are much exaggerated; but, inasmuch as commerce and 
travel are mostly confined to the torrid and temperate zones, 
this p/ojection is used very extensively. On the ocean 
especial] V, it is indispensable. 



66. Location on a Plane. — As a preparation for the 
comprehension of latitude and longitude, as well as of 
■' vStandard Time," it would perhaps be difTficult to find any- 
thing in the way of an exercise better than the following: 

Require the pupils to subdivide on paper a drawing of 
any plane rectangular surface, say the floor of the classroom 
(Fig. 3). It may be numbered as shown in the figure, or in 
any other vSuitable manner. The teacher'will of course notice 
that the two heavy lines at right angles represent for the 
floor just what the equator and the prime meridian represent 
on a globe, a Mercator's projection, or on an ordinary map. 
This drawing can be placed on a blackboard or on a large 
sheet of manila paper and used for general class exercise. 

In using this, the pupils may be required to find very 
promptly points indicated by the teacher; as, N Id, W 4; 
vS7, E5; vS 11, W IT); etc. Very soon the teacher should 



^8 



PEDAGUCUCvS OF GEOGRAl'lIV 



§ ^ 



introduce the word north, instead of N, cast instead of E, 
etc. This will tend to make the pupils quick to recognize 
directions on maps and globes. 

Interest and variety may be added to the exercises by 
employing certain fictions, such as imaginary sea voyages, 
railway travel, vessels sunk by storms, cities located, etc. 



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*1 "^l N -1 "^ "S *1 •n "^ *<*<** 5 



If, later, lines be drawn to show the tropics and the polar 
circles, the pupils may be made very familiar with the tem- 
perature that prevails in different zones, ^s well as with the 
alternation cf the seasons. Such questions as the following 
will be quickly answered by the average pupil, if he be 
taught to understand that his diagi'am represents the earth's 
surface : 

"Where should one expect the warmer climate, at S 25 or 
atN40?" "Why?" 

" Point out places that have summer in June; places that 
have winter in June." 

' ' There is a city at S 23, W 4 o, and another at N 41 , W 74 ; 
which should be warmer in simimer? Which has noon first 
on any given day ? " 



g5 PliDAGOGlCvS OF GEOGRAPHY. 7'J 

"A ship was sunk tit vS 50, W 50; point out the place. If 
the time was August 15, what season was it at that place ? " 

"I have a friend that lives at N -li, WG'J; indicate the 
place." 

" In what month does winter begin in Japan ? in Australia ? 
in Argentina ? " 

The usefulness of this, and of every other exercise, will of 
course depend almost entirely on the teacher. If he knows 
just what he wishes to accomplish; if he introduces the 
proper exercises just at the right time, and persists with them 
sufficiently; if he understands his subject thoroughly, and 
handles it skilfully, the impressions will be clear, sharp, and 
lasting, and the benefit very great. 

Obviously, it would be aside from the purpose of this 
Paper to do more than indicate some of the objects aimed at 
in the intelligent teaching of geography, and to suggest a 
few of the many methods of attaining these objects. The 
field is so wide, and it contains so many matters of practical 
educational importance, that the teacher is certain to find 
confusion in an "embarrassment of riches;" and it requires 
a wide acquaintance with the requirements of life, as well 
as careful reflection and judgment, to decide what to omit. 

67. Plan of tlie Classroom Di-a^vn to Scale. — Avery 

interesting variation of the foregoing exercise is to draw a 
few rectangular surfaces to scale, and to represent in cor- 
rect position the various objects that occupy those surfaces. 
For this purpose, no better surface than the floor of the 
classroom (Fig. 4) could possibly be found. 

Let us suppose that its dimensions are 24 feet by 30 feet. 
If we make each i inch in the drawing represent 1 foot in 
the reality, our plan will be 3 by 3| inches — a convenient 
size. The various articles of furniture must be located by 
actual and careful measurement. Thus, if the teacher's desk 
is 3 feet long and 2 feet wide, its .size in the drawing will 
be fin. X { in. If it be placed 3 feet from the front of 
the room, and equally distant from the sides, it will stand as 
shown in the diaoTam. 



so 



i>]':l)AG()GiCvS of geograpuv. 



^ ^ 



There are many exercises of i^reat value that may be had 
with the drawing- after it is finished. Thiis, the teacher may 
direct the pupils to find out from their drawing- how far it is 
from her desk to seat 7, 11, etc., and require that the answers 



i?^^'j:W\mi?M4i4i^mm^ 




@ @ @ ® 



@ @ @ ® 



@ @ 



@ ® 



@ @ @ ® 




© @ @ @ 



@ @ @ @ 



© @ @ 



o 



Plaf/crr, 



Fig. 4. 



be confirmed by actual, measurement. This is the exact 
equivalent of finding how far it is from one place to another 
represented on a map. 

This work may be profitably continued with outside areas ; 
as, the school yard, the block, the village, etc. Committees 
of pupils may be sent to measure the distance to certain 
specified points, and the work of making a map may be con- 
tinued from dav to dav until it is finished. The teacher 



§ 5 PEDAGOGICS OF GEOGRAPHY. 81 

may have a large sheet of paper suspended against the wall, 
and on this the work may be done to a larger scale than is 
used by the pupils. The fascination of this kind of work 
will grow with marvelous rapidity, and it would be difficult 
to find any other exercise that is valuable in so many ways 
as is this. 



THE MAKIXG AXD RECORDING OF 
OBSERVATIONS. 

68. The Bicycle in Geography. — He must be a far-see- 
ing man that can accurately gauge the wide and multiform 
influence of the bicycle on the development of the race. 
This vehicle has come to stay, and has compelled an aston- 
ishing readjustment of things to new conditions. Many 
forms of business long established have been greatly affected 
by it, and many others have come into existence to meet 
new demands caused by its advent. 

The writer recently overheard a conversation between a 
jeweler and a clothier in which each blamed the bicycle with 
being the cause of depression in his business. " My trade is 
nearly ruined by the machine," said the one. "The fathers 
and mothers that formerly bought watches, rings, and dia- 
monds for their sons and daug-hters, now give them bicycles 
instead." "Yes," replied the other, "and thousands of 
young men and women are expending money for clothes 
that we do not furnish. The wheel has caused them to lose 
the art of dressing. Dressing for appearance is being dis- 
placed by dressing for ease and comfort." 

The horse, discarded by the electric car, and supplanted 
by the bicycle and the automobile, is, like the American 
bison, menaced with extinction. The rapid spread and 
enduring tenure of the ancient Roman power has been 
attributed to the fact that wherever they went they caused 
most excellent roads to be made. The bicycle is causing 
the same beneficent work to be done. It is possible now, in 
all kinds of weather, to ride for htmdreds of miles continu- 
ously on roads that are well nigh perfect. The mission t>f 



83 PEDAGOGICS OF GEOGRiVPHY. § 5 

the wheel, to compel the making of roads, is being accom- 
plished with a promptness and a thoroughness of which the 
Romans were utterly incapable. 

It is widening oiir actual horizon, and making observers 
of us ; our knowledge of local geography is no longer con- 
fined to an area of a few square miles, but in many cases it 
has been extended beyond the limits of the rider's own 
county and state. Indeed, it is no longer regarded as a 
notable feat to make a journey awheel from the Atlantic to 
the Pacific in our own country, or to explore in the same 
way all the countries of Europe. 

69, Tlie Wlieelmau as a Teaclier of Geography. 

Every wheelinan must become in some measure both a stu- 
dent and a teacher of geography and its allied sciences. His 
membership in the "League of American Wheelmen" or 
in the "Good Roads Association" enables him to obtain 
reliable maps covering any tour he may wish to make; and 
not only he, but his friends as well, become interested stu- 
dents of the topography of any prospective trip before it is 
begun. But it is when he returns that he really becomes an 
enthusiastic teacher of geography. Like the tale of the 
"Ancient Mariner," his also is one that must be told. It is 
a vivid tale, and interesting, for he knows whereof he speaks. 
His map is no longer a mere map; it is rich in sug'gestions 
of personal experiences of every kind; it is, so to speak, a 
chapter of condensed autobiograph}^, and a sight of it at any 
future time will recall the most delightful memories. He 
cannot, then, avoid being an earnest and eloquent teacher, 
and he has no difficulty in finding and holding his audience. 
Ulysses, when he returned from his ten years of wandering, 
could scarcely have been more entertaining than the wheel- 
man after one of his long, delightful trips. He spreads the 
contagion of travel; he is not content until he has induced 
his friends to go with him and see what he lias seen. 

And just here is an important principle in pedagogics; No 
one can teach geograpliy so well as an observant and intelli- 
gent traveler. His teachings have an interest that is strongly 



§ 5 PEDAGOGiCvS OF GEOGRAPHY. 83 

human; he deals miieh with man and tlie matters that 
strongly affect human welfare. How delighted we are 
to listen to one that has actually seen the myriad sights 
of travel, — has "been a part of that wdiereof he tells." 
When Othello finishes his tale to Desdemona concerning 
the wonders he had seen, she thanks him. Remarking 
further on the effect of his story, Othello says, " She 
thanked me, and bade me, if I had a friend that loved her, 
I should but teach him how to tell my story, and that would 
woo her." 

What an admirable teacher ol the natural sciences in 
general, and of geography in particular, would von Hvmi- 
boldt have been, or Darwin or Baker or Layard or Living- 
stone or any others among those learned "globe trotters" 
whose writings we find so charming. 

TO. 8uTve.viii^" AVitli ]>ieycle and Cyclometer. — In 

an admirable article with the foregoing title a cycling friend 
of the writer gives, in a late number of the " Mechanic Arts 
Magazine," a minute and systematic account of what maybe 
done in the way of recording the facts of a trip on a bicycle. 
The author has kindly permitted the use of his article in any 
way that may bt- deemed helpful to the students of this 
Paper. Its length is the only reason for not inserting it 
entire. 

The article gives the notes recorded and the details 
of scenery observed during a trip froin Wilkes Barre to 
Shawnese lake, in Luzerne county, Pennsylvania, and it 
shows the maps constructed from those notes. 

71. Tlie Cyclometer. — "Now, let its consider," says 
the author, " the method of procedure by which the bicyclist 
may become a surveyor and thereby able to convert the 
results of each trip over a new road into a permanent record 
for future use. In the first place, a word about the cyclom- 
eter and its value as a surveying instrument. 

' ' A cyclometer is not what mathematicians would call an 
instrument of precision like the transit, the level, or even 



84 PEDAGOGICS OF GEOGRAPHY. § o 

the surveyor's compass. It will record with an error of 
about 1 per cent, when working at its best, and under certain 
circumstances the error will be increased to 3 per cent. This 
error is due to the relation between the bicycle wheel and 
the number of revolutions that will cause the cyclometer to 
record 1 mile. The usual cyclometer requires 720 revolu- 
tions of a 28-inch wheel, in order to record 1 mile; but owing 
to the deflation of the tire and the weight of the rider, the 
wheel may be but 27.5 inches in effective diameter, and the 
cyclometer will record 1.019 miles for each mile ridden, or 
101.9 miles for each 100 miles. In addition to this error, 
the bicycle actually travels farther than the true length of 
the road itself, owing to the fact that the rider continually 
crosses and recrosses the road in order to select the best 
parts for cycling; and this error, varying as it does accord- 
ing to the character of the road, will amount to about 2 or 
3, per cent. more. Therefore, before we start on our survey, 
we w411 assume that our cyclometer measurements will all 
be 5 per cent, in excess of the actual distances traveled. If 
the bicycle surveyor be an experienced rider, his map may 
be so plotted that grades and conditions of road may be 
readily expressed, and other information never found on the 
most accurate of maps may be added as a guide to the future 
traveler. " 

73. The jS"ote Book. — "The next detail to consider is 
the note book. This should be long and narrow, with two 
parallel lines ruled down the center of the page to represent 
the road. Stenographers note books serve the purpose 
admirably ; these are about 44- inches wide and 8 inches long, 
and are ruled across the page with lines about ^ inch apart; 
the two parallel lines down the center of each page can be 
ruled with either pencil or pen, and the book is then ready 
for the trip. A piece of board, the same size as the book, 
should be secured to the handle bars, and the book laid on 
and bound fast with rubber bands. A bicycle watch on the 
handle bar is also a great convenience, but by no means a 
necessitv. 



§ 5 



PEDAGOGICvS OF GEOGRAPHY. 



85 



"The arrangement will now look somewhat as in Fig. o. 
At a is the cyclometer, the 
record of which should be 
easily read by leaning over 
the handle bars ; at I? is the 
note book; and at c is the 
watch, which will act as a 
check on the cyclometer 
and grade notes. Now, 
we will assume that the 
bicylist is out on a trip 
with a number of other 
enthusiasts, and, therefore, 
will be imable to stop and 
make any individual meas- 
urements of the roads and 
landmarks which he passes. 
All notes must be made 
awheel, and inforiuation 
recorded without slacken- 
ing speed. Before he starts, the register of the cyclometer 
is observed, and written on the lowest line of the note book 
and is found to be :2,388.8 miles, as shown in Fig. G. In 
recording subsequent cyclometer readings it will not be 
necessary to note the thousands and hundreds of miles, 
except when these, figures change." 




Fio. 5. 



73. Tlie jVotes. — " The surveyor starts out through the 
main street of Wilkes Barre, and as he crosses the river he 
notes that his cyclometer reads 2,389.05 miles, and on the 
second line from the bottom he marks this record, as shown 
in Fig. (i, and at the same time draws two wavy lines across 
the road to indicate that it was while crossing the river that 
he recorded this reading. Soon he arrives at the Kingston 
cross-roads, and there turns to the right; his cyclometer 
reading is recorded as 00. '24, and, branching from the nght 
of the central column of his. note book, he indicates the road 
he takes with an arrowhead as shown, while on the left he 



86 



PEDAGOGICS OF GEOGRAPHY 




S-'d<-v^ , <f-4- " ^^- ^^ ^^^ ^^'^^' 

FIG. 0. 



shows a similar cross- 
road with no arrow. 
Observe, also, that his 
note book does not 
show this cross-road 
as branching at a 
right angle from the 
road he is traveling, 
but the cross-road is 
drawn according to 
his judgment, at about 
the angle it actually 
makes. On the oppo- 
site side of the road, 
on the corner, is an 
old tavern, and he 
marks a rectangle to 
indicate it in his notes. 
Village streets branch 
from the main road 
through Kingston, and 
as he passes he in- 
dicates these in the 
notes at cyclometer 
readings !)0. 139 and 
90.44. At 90.99 he 
arrives at the village 
of Dorrancc, takes the 
left branch, and rides 
straightaway to 91.85 
— in the village of Lu- 
zerne — where he takes 
the left branch for a 
little way and then at 
92.25 the road itself 
turns slightly to the 
right. 

"This indication of 



§ 5 PEDAGOGICS OF GEOGRAPHY. 87 

a bend in the road is made simply by drawing, in the cen- 
tral column, two straight lines, intersecting at about the 
angle of the bend of the road, as shown in Fig. O. In 
general practice, slight bends in either direction are not 
considered; but, where a bend or a branch of the road is 
but a trifle less or a trifle more than a right angle, this 
shortage or excess should be indicated by a plus or minus 
sign, as shown on the branches at Kingston and Dorrance 
90.24 and 00.09. At 92. 70 'the road bends to the left, and 
at 02.80 it turns to the right, while at 93 it turns at right 
angles as indicated. At 94.15 the road forks, and the tourist 
takes the right fork, as indicated by the arrow. Soon he 
crosses a stream, as indicated by the wavy line at 94.58, 
and y^-Q of a mile beyond he passes through Truckville, and 
takes the right fork of the road out of that village. At 96.72 
there is a branch road back and to the left, which the rider 
takes. At 97.93 there is a similar branch road to the left, 
and at 98. 10 there is a branch road to the right in the village 
of Dallas. 

"We have considered here only the distances and the 
roads, while on the left of the note book are some entries 
of landmarks that give additional value to the directions 
when used by some one else than the original surveyor. 
The cross-hatched line at 92.25 indicates that there is a rail- 
road crossing there. At Mill Hollow is shown a small rect- 
angle to the right of the road, while marginal notes on the 
left of the page indicate what stands in the place so marked. 
The time of arrival at, and departure from, different places, 
as inarked on the left of the page, is also of value, as show- 
ing the general character of the roads traversed. For 
instance, from Wilkesbarre to Kingston, a distance of 
1^ miles, covered in 7 minutes, indicates a good piece of 
fairly level road, and the same may be said of the stretch 
from Kingston to Luzerne ; but the distance from Luzerne to 
Ice Cave, 2^ miles, required 35 minutes, which, together 
with the fact that a rest of 15 minutes was taken at Ice Cave, 
would indicate a rough road traveled. The circles with dots 
in the center indicate the position of the sun, at various 



88 PEDAGOGICS OF GEOGRAPHY. § 5 

points on the road, so that, with the notes regarding the 
time of arrival at different stations, a fair idea of the points 
of a compass may be obtained. At the start the sun was 
directly behind and shining down the street at 9 : 30 in the 
morning, which would indicate that the road ran northwest 
and southeast. From Kingston to Luzerne the sun was on 
the right, while, before taking the right fork beyond Truck - 
ville, the sun was on the left. At Dallas, where stop was 
made for dinner between noon and 1 o'clock, the sun was in 
the direction shown by the circle and arrow, which may be 
considered as due south. Other details of the notes will be 
considered during the explanation of the plotting of the 
map. 

"As a usual thing it is desirable that the bicyclist surveyor 
should travel homeward by another road, so as to continue 
his notes and make his round trip a complete siu'vey without 
repetition ; but we will not concern ourselves with the return 
trip at present, but proceed to plot our map from his notes 
here given." 

•74:. The Map. — "A scale of 1 inch to the mile is a 
good size for practical purposes, and we will proceed to draw 
a inap on this scale. It is apparent from our notes that the 
road from Wilkes Barre to Kingston, 1^ miles in length, is 
practically straight ; therefore, we measure off 1 i inches on 
our drawing paper and lay off this piece of road, marking in 
small numbers the beginning of it as 2,388.8 and the end of 
it 90. 24, as shown in Pig. 7. Somewhat more than i mile out, 
we cross the Susquehanna river; therefore, at 89.05 we draw 
the river crossing the road at right angles. At station 
90. 24 we indicate the road branching to the right and left, 
and continue the right branch until it measures 3 miles from 
the beginning. This takes us to the village of Dorrance, 
which is marked in our notes as 90.09, where we turn to 
the left at an angle slightly in excess of a right angle, as 
indicated by the plus mark, and plot our road to 91.85; here 
the road forks to the left, and we continue through Mill 
Hollow, a small settlement that evidently takes its name 



S5 



PEDAGOGICS OF GEOGRAPHY. 



89 



from an old mill on the right of the road, as indicated by 
the notes. Here the road crosses a small stream, turns to 

the right, and at station 93 takes 
a sharp turn at right angles to the 
left, which, with a subsequent half 
turn to the left, and two half turns 
to the right, brings us to another 
small settlement called Ice Cave, 
94.15. About 2 miles from here, 
after crossing a small creek we 
arrive at Truckville, indicating the 
creek by a wavy line, and then 
plot the road to Dallas. The creek 
may now be continued parallel to 
and on the right side of the road 
and up to 95.63, where it crosses 
the road to the left side, but re- 
crosses and returns almost immedi- 
ately. "When the cross-road at 
Dallas is plotted, particular atten- 
tion must be g'iven to its direction, 
as, according to the indicated posi- 
tion of the sun in the notes, this 
road should run north and south, 
and any errors in the previous lines 
should here be corrected. 

" The rest of the road up to the 
lake is similarly plotted and the 
road around the lake sketched in ; 
then the lake itself may be drawn, 
as the road extends along its border 
and is governed largely by the out- 
line of the lake itself. Thus, a complete and satisfactory sur- 
vey of the road may be plotted in an hour, from notes which 
were taken without the slightest loss of time on the trip." 




75. Tlie EiiA-ii'oiinieiit. — "Subsequent trips and sim- 
ilar surveys of other roads in the vicinity, when plotted, 



90 



PEDAGOGICvS OF GEOGRAPHY. 



§5 



SHAWNNt LAHC 



will be found to fit in one with another, and thereb}' make a 

most satisfactory map, 
as shown in Fig. 8. The 
bicyclist is rendered 
more observing; by work 
of this character ; he sees 
every detail, he notes 
every bend in the road, 
and in a short time he 
unconsciously searches 
for some landmark by 
which he can identify a 
certain, piece of road, 
either for his own or 
some one's else use. In 
making" notes on a trip, 
it is always wise to 
assume a certain defi- 
nite angle which will 
indicate a bend in the 
road. 

' ' Where a road crosses 
or changes its direction 
at right angles to the 
, course pursued by the 
rider, the record is not 
difficult; and even where 
the deviation or crossing 
is at an angle of 45°, 
there is little chance of 
error; but for angles 
between these it requires a trained eye to judge them with 
accuracy, and they should be recorded as 45° or 90'' turns, 
according to which they are nearer to; but a slight deviation 
from a right angle should be indicated where such exists, 
and a plus or minus sign marked, in order that the figures 
may plot more satisfactorily. Alwa5'S note everything 
possible. On a road map a landmark is often more important 




Fin. S. 



§ 5 PEDAGOGICS OF GEOGRAPHY. 91 

than roadbed or distances. At every cross-road, fork, or 
abrupt turn, identif}- a landmark. This may consist of an 
'old tree,' a 'church,' a 'red barn,' a 'stone mill,' or any 
object which may in a few words be described as a monu- 
ment to locate a particular point in the survey. Always 
show streams of water when the}' run parallel to, or across, . 
the road, and indicate which wa}- they flow, for such details 
give information as to the grade. Where a road is through 
a thick wood, indicate the fact, as such a road is seldom 
ridable after heavy rains, and is usually in good condition 
when other roads are dry and sandy. Be sure to show 
springs, water troughs, etc., as they serve as resting places 
where refreshments may be taken, and at the same time act 
as landmarks to assure the traveler that he is on the right 
road according to his map and directions. The complete 
bicycle survey of this road, as far as recorded in our notes, 
is shown between a and b in Fig. 8, together with other 
surveys made of neighboring roads. Note the location of 
streams and connections from streams of one survey to 
similar ones in the next, thus completing these little water- 
ways and showing the grades of the locality. All of this 
may seem a great deal to do when a man is on a pleasure 
trip, and, to a certain extent, it is; but it gives him educa- 
tional as well as recreational benefits from the trip, and he 
is putting his efforts to practical use. In a ride of 18 miles 
it certainly will not require much effort to make two or 
three note-book entries each mile, when the book is 
strapped in front ready to receive them, and yet that is 
about what the entries average in the accompanying illus- 
tration. Let the scheme once be tried, and, after an honest 
effort at making a bicycle survey, few men will give iip the 
work, as it possesses a fascination second only to bicycling 
itself." 

"70. '*Heiniatkiiii(le. '''' — The student may perhaps 
imagine that too much importance is attached to home 
geography, — Hciinatkitndc, "home knowledge," as the 
Germans call it, — but the latest and most approved methods 



92 PEDAGOGICvS OF GEOGRAPHY. § 5 

of teaching" the subject would warrant even greater emphasis 
than has been put upon this early work. The great revolu- 
tion in pedagogical methods that was inaugurated by Rous- 
seau about a century ago, has been spreading and intensifying 
ever since, until now it is axiomatic that our children must 
be taught things, not words, realities, not mere ideas. Rous- 
seau's words are eminently worthy of quotation : 

111 every study signs are worthless without the ideas they represent. 
Nevertheless, our children's study is confined to signs; they rarely 
become able to understand the things themselves. While we are 
endeavoring to give them a description of the earth, they make the 
acquaintance of the map ; they learn the names of cities, countries, 
and rivers, of which they have no adequate conception. To them 
these things are nowhere except on paper; they are not seen. There 
is nothing to indicate that they have any real existence. 

The city in which the child lives, the country home of his parents, 
these should be the first two points of departure in geography ; then 
should follow the features about them, — the streams in the neighbor- 
hood, the position of the sun, the mode of finding one's way by geograph- 
ical directions. The child should make a map, however simple, of his 
own, which at first may contain only two points, and to these may be 
added others as instruction proceeds, and as he learns to estimate 
distances and positions. Never place the sign before the thing, unless 
it is absolutely impossible to produce the thing itself; for the sign 
absorbs the attention of the child and causes the thing it represents to 
be forgotten. Things! Things I I cannot often enough repeat that we 
give too much importance to words; by our talkative education we 
produce prattlers. 

It is undeniable that geography, of all studies, is the one 
that most needs sensualization and a rich store of funda- 
mental percepts. Maps and all other symbolizing apparatus 
are of little value unless transition from them to the realities 
they represent has been made easy by a wealth of accumulated 
memories of things that have actually been before the senses. 

Comenius strongly urges that instruction .should begin 
with sense perception, with observation of real objects; 
because real knowledge grows from .sense perception and 
from that alone. He insists that for this reason lessons in 
geography should at first be object lessons and observati(jns 
of the things immediately around home. 



§ 5 PEDAGOGICS OF GEOGRAPHY. ii3 

7 '7. Observation of tlic 8un"'s Apparent Motion. 

Comparatively few persons are thoroughly familiar with the 
mutual relations in position and motion between the earth and 
the sun. It seems to be a subject of considerable difficulty, 
but in reality it is quite simple. At any rate, it is a matter 
that every teacher should fully understand; for, unless he 
does, it is certain that his pupils will not. It is not here 
meant that the ordinary student of g-eography should be 
taught anything more than the general facts relating to the 
simplest and most obvious of these motions and relations — 
the geographical pliase of the matter. The refinements and 
difficulties should be avoided, for they belong in mathemat- 
ical astronomy, not in geography; even the simpler matters 
are likely to be troublesome unless they are handled with 
much skill, and are deferred until the pupils are quite mature. 
There are, however, many simple observations bearing 
upon the subject of mathematical geography. These may be 
begun early in the geographical period, and although the 
pupil may be incapable of fully imderstanding the reasons 
that account for the observed facts, he may and should be 
familiar w'ith the facts themselves. Thus, suppose that the 
sun's advance north and its retreat south along the noon 
meridian be made a matter of observation and record from 
day to day. If in the schoolroom there is a window looking 
toward the south, the pupils may be required to mark at 
12 o'clock each day the point farthest north that the sunlight 
reaches. Suppose that the observations are begun at the 
opening of school in September. It will be found that the 
limit of shadow is retreating toward the north, and that this 
continues to be the case until December 21. Then there 
seems to be a pause of several days. This means that the 
sun is shining vertically on the Tropic of Capricorn. This 
point of pause maybe marked "Tropic of Capricorn." The 
tropics are so called from the Greek rpomKog, tropikos, "hav- 
ing reference to a turning. " This is the beginning of .sum- 
mer in the southern hemisphere, corresponding to our 
June 21. Require the pupils to find on their maps the coun- 
tries in the south temperate zone having the season that is 



'J-i 



Pl^>DAGOGICvS OP GEOGRAPHY 



N 
Tropic of Cancer. 



June 21 r 



Solstice. 



<, ^ «^ Equator. ,, „, 
Sept. m . — [ — I — Ma r. 21 



Equinox. 



Eq It i n ox. 



to be ours six months later. Ask them to imagine and 
describe what the people of those countries are doing, and 
have them realize the facts about the length of day and 
night there and here. 

If this work be continued from day to day and the records 
carefully made, a very satisfactory analcniina., as it is called, 
may be made, and a drawing in cor- 
rect scale may be constructed by the 
pupils. Such a drawing with inter- 
mediate markings omitted is shown 
below. 

It should be observed that the mark- 
ings made on the floor must be reversed 
in drawing an analemma; for when the 
sun is farthest south, the shadow limit 
is farthest north, and the reverse. 

This kind of observation may be 
made from the shadow of a pole ten or 
more feet high planted erect in the 
school yard. Its shadow at noon will 
point north, and from this the other 
points of direction may be fixed in 
such way as to make them very famil- 
iar to every pupil. Moreover, a fairly 
accurate sun dial may be marked 
around such a pole by indicating the 
hour lines. This will soon lead to the 
discovery that such lines are variable, 
changing somewhat from month to 
month. When the children learn that this is true, their 
inquiries will lead naturally and directly to the methods of 
constructing sun dials that .shall be accurate for all seasons. 
Very valuable information wall be elicited, provided the 
teacher will properly direct their curiosity. Very exact 
details on the subject of "dialing" can be found in any good 
cyclopedia, and by pursuing this matter, the teacher will 
be able to benefit very greatly, not only the pupils but 
himself. 



Solstice. 
-Dec. SI. 



Dec 21t 

Tropic of Capricorn . 

S 

Fig. 0. 



PEDAGOGICvS OF GEOGRAPHY. Do 



(JRAPIIIC GEOGRAPHY. 

78. Tlie flaking of Maps. — All authorities on the 
methods of teaching geography seem to be agreed as to the 
great value of map-drawing. It is regarded as a very useful 
and important, nay, an indispensable featiu'e. They are 
not, however, tmanimous about its purpose and methods. 

Some advocate the teaching of map-drawing for the sake, 
in large measure, of the training in drawing; and their limit 
of excellence is the finished elegance and accuracy of the 
expert chartographer. During the writer's visits among the 
large graded schools of some of our great cities, he has seen 
hundreds of maps of marvelous excellence and exactness 
made by the pupils. Principals and teachers are invariably 
very proud to show such work, and they seem to believe that 
such maps are evidence of good work in the teaching of 
geography. Anunig these maps were to l)e found represen- 
tations of great land masses, as vSouth America, in all sizes 
down to less than a scpiareinch. Hours and even days were 
required to finisli them; and both to execute them and to 
see them properly a magnifying glass was needed. In them 
were shown details in bewildering minuteness. Any one 
that saw the educational exhibit at the Centennial Exposi- 
tion in 18T0 at Philadelphia, or that at the World's Fair in 
1893 at Chicago, will doubtless remember having examined 
similar work and doubted whether it could possibly have 
been done by ordinary school children. 

Other authorities advise against work of this kind, 
and insist that it furnishes little help in the real teaching of 
geography. They say that a pupil may be taught to make 
such maps in the utmost perfection and escape learning any- 
thing of value in practical geographical knowledge; very 
much as one may copy in admirable fashion the words of a 
treatise on any learned subject, and yet not get a single idea 
that he did not have before he began. In the opinion of 
these authorities map-drawing should be practiced for the 
purpose of illustrating geographical facts and principles, and 
the drawing itself may be rude and rapid, provided it effects 



90 • PEDAGOGICvS OF GEOGRAPHY. § 5 

the purpose eoiitemplated. For example, a teacher may 
wish to show the commercial advantages that arise from the 
fact that any great city is situated where it is, or the reasons 
why a certain railroad should follow a particular course 
through a country. In doing this, it is necessary to indi- 
cate only the means of exit for the commerce of the city 
tinder consideration, the mineral, agricultural, and lumber- 
ing fields around it, and the needs of neighboring market 
centers. In the other case, the relief of the cotmtiy trav- 
ersed, the centers of industry and population reached, the 
productive areas and undeveloped resources provided for, 
may be rapidly sketched, and thus the pedagogic purpose 
of the drawing is fully accomplished. Another argument 
in favor of this view is that few pupils and fewer teachers 
can make an elaborate map, while any one can construct 
maps of the kind just indicated. 

71). The Intermediate Tiew. — As is the case with 
nearly all other subjects, there is with respect to map-draw- 
ing a "golden mean" that is better than either extreme. 
Undoubtedly there are good reasons for cultivating an 
ability to make finished and accurate drawings of every 
kind, maps included. But it is to be remembered that the 
educational usefulness of maps as a help in geographical 
teaching is not very great, although in some other respects 
they may be of the very highest value. 

On the other hand, the skctcJiing of maps is an indispensa- 
ble aid, and should be much practiced at every point in the 
geographical work in school. It is the kind of map-drawing 
that is to be employed in actual later life. 

80. The Resolutions of the German Geographical 
Congress. — In consonance with the foregoing view, the 
following resolutions adopted by a late German Geograph- 
ical Congress may be helpful as a guide to the teacher of 
geography. They were the outcome from an animated and 
thorough discussion. 

1. The German Geographical Congress recommends drawing in 
geographical instruction as an indispensable means to the promotion 



§ 5 PEDAGOGICS OF GEOGRAPHY. %' 

of clear intuitions, and :is a powerful aid to iiwakening' the self-activity 
of pupils. 

2. It declares itself most positively against the widespread evil of 
setting pupils to draw maps as a home task without fitting them for 
the work by a gradually progressive training. 

3. It condemns the use of straight lines to express the lines of a 
map (Lohse's method), since this plan is not adapted to develop the 
pupd's sense of form, but rather debases his taste in regard to map 
representations. 

4. It most positively condemns the systematic carrying out of the 
so called " constructive method," since it requires a system of artificial 
aids (lines and points), the knowledge of which is in the main of no 
value to the pupil, and heavily burdens his memory in a useless way. 

5. It condemns special preliminary courses in topographical draw- 
ing as aside from the purposes of the common school. 

6. It recommends the method of free sketches of single terrestrial 
spaces as reproductions of typical relations studied from the map, since 
these can be adapted in amount of detail and mode of execution to the 
capacity and skill of the pupils. 

The student will observe that by these resolutions map- 
drawing" is regarded as indispensable as an aid in g-eograph- 
ical teaching, bitt the pupil should not be sent away from the 
classroom with a task in drawing" to complete by himself. 
On the contrary, the work should be made a class exercise, 
in which the map is made only as fast as the ideas to be repre- 
sented are developed by the cpiestions and answers of the 
pupils and teacher. No map should be drawn in which reli- 
ance is placed upon straight guide lines or geometrical 
skeletons in measured straight lines. The reason for this 
prohibition is that it defeats the most important object 
sought in the exercise, that of developing the ptipil's sense 
of form. By the fifth resolution, it is clear that the Con- 
gress would discourage any striving after chartographic per- 
fection, since it advises against any preparatory course of 
drawing in which skill in the art for its own sake is the 
object; and by the last resolution, the student is advised to 
make sketches of parts of a country or state merely as a 
means of illustrating some point or principle of importance. 

81. Vie^vs of the Teacliers and Inspectors at 
Vienna. — In confirmation and support of the foregoing 



!»8 PEDAGOGICS OF GEOGRAPHY. § 5 

views, the student should eoinpare llie eonelusions reached 
at a meeting of the teachers and school inspectors in the 
capital of Austria, a country second to none in Europe for 
the excellence of its geographical teaching. 
Among other matters, it was there decided: 

That a moderate application of drawini^- in teaching geography is 
pedagogically valuable, Ijut is not indispensable as a means to the 
right apprehension and memorizing oE the map. 

That drawing is only a means, never an end in itself. 

That the geographical drawings of jnipils should not be tirged 
beyond their acquired skill in general drawing. 

That the representability of geographical ideas and the special aim 
or purpose of the instruction in geography should determine the kind 
of drawing required. 

That the drawing should be restricted to geographical specialties, 
such as single rivers, relative positions of places, mountains, slopes, 
plains, basins, etc. 

That political boundaries, drawn as mere outlines, and without ref- 
erence to the position of enclosed places, commercial and industrial 
activities, or natural resources, should be excluded. The same prohi- 
bition is made against drawing entire coast lines, countries, and grand 
divisions. 

That the requirement should not be made that, at the end of a term, 
a year, or any other period, the pupils should by way of review be aljle 
to draw from memory the maps studied during the period. 

The student will notice that somewhat less insistence is 
here placed upon the value of map-drawing than is the case 
with the German Congress; but that is one of the things 
that must be expected with regard to all matters of opinion. 
It should be remembered, too, that the Germans, being the 
map-makers of the world, would naturally emphasize the 
importance of that in which they excel all other people. 
And on the other hand, we may safely assume that the 
Austrian educators would be disposed to disparage some- 
what an art in which some other nation surpasses them. 
Here, as everywhere el.se, the thoughtful student will seek 
the truth between the extreme views of rivals. Let ns hope 
that our teachers may before many years carry the same 
degree of enthusiasm and excellence into this work that the 
American people habitually do into other matters that are 



§5 PEDAGOGICS OF (tEOGRAPHV. '.)9 

in process of development. In the natural search after 
models that we may imitate, we can j^et what we require 
nowhere so well as in the practice of the schools of Central 
Europe. They have approached scientific precision in 
teaching' geography and the other natural sciences more 
closely than any other people in tlie world. 

S2, Map-Ske telling : Dimensions, Area, and Relief. 

In order to illustrate the manner in which map-sketching 
should be used as an aid in teaching geography, let us sup- 
pose that a class is engaged in studying the state of Penn- 
sylvania. Naturally, the first thing to consider would be its 
outline, its dimensions, its area, and its relief. A free- 
hand drawing should therefore be made of its boundaries, 
and their lengths may be written along the several lines 
that represent these boundaries. The inountains and 
rivers may then be sketched in, and as the work pro- 
gresses, names and important facts should be given. 
These mountains and rivers will reveal the slopes, the 
highlands, and the valleys, and the pupils may be called 
upon to trace the "divides," or watersheds, that separate 
contiguous basins. If there are regions favorable to agri- 
culture, lumbeiing, manufacture, mining, or commerce, the 
slopes, valleys, and mountains will show where they prob- 
ably are, arid the pupils may be called on to .say where these 
several features are to be sought. Tliis will introduce the 
elements of cause and effect, without which geography as 
well as the other natural sciences cannot be well taught. 

vSuch a map, with nothing more on it than what is 
indicated above, may be made the basis of several very 
interesting and valuable lessons, provided the teacher 
thoroughly understands his subject and has properly pre- 
pared himself for the lessons. For example, the pupils 
may be asked to find out how many days it will take 
an army, marching at the rate of 130 miles a day, to cross 
the state from east to west, and how many, from north 
to south. How many farms of 100 acres each the state 
contains is a matter eas^^ to find out when it is known that 



KM) PEDACOCllCS Ol- (;E()GRAPIIV. ^5 

four such farms occupy a square mile, and that the laud area 
of the state is about 45,000 square miles. The population 
of the state and its area being given, the population per 
square mile may be found, and later, a table may be made 
showing the comparative density of population of Pennsyl- 
vania and various other states; and these figures may then 
be compared with that of certain indicated foreign countries. 
This is the only w^ay to interest children in statistics, some 
varieties of wdiich are of extremely high value in education. 

A few of the higher and lower points of surface may 
be marked on the map, although this is not a matter of 
the greatest importance. In the absence of such marked 
points, the pupils can find them by observing the direction 
in which the rivers flow, and by knowing that they must be 
sought in the lowest valley levels, and that rivers are least 
elevated at the point w^here they enter the ocean or other 
large body of water. 

Our map so far is all the more instructive in being empty 
of confusing details. This confusion is one of the w^orst 
features of modern textbooks. Most people are prompt to 
condemn a geography if it happens not to contain a map 
showing the little country village where they were born. 
But a map that does this has no value as a means of teach- 
ing philosophical geography. 

83. liater Ijessons. — Within an outline sketch of the 
state other important geographical facts may be indicated 
and discussed, and the necessary drawing may be done by 
the pupils in turn. Thus, the location of the various species 
of mineral wealth, — coal, iron, mineral oil, etc., — the tim- 
bered and agricultural areas, the situation of deposits of iron 
with respect to their neighborhood to the coal used in smelt- 
ing them, the means of exit to market for the products of the 
lumber regions, the inland waterways available for commerce, 
and the nature of the products carried, the trunk lines of -rail- 
way and their tributaries, the location of the chief manufac- 
turing cities and their various industrial activities — these and 
many other matters of importance may be the subjects of a 



§ 5 PEDAGOGICS OF GEOGRAPHY. lol 

series of lessons for which textbooks should be used merely as 
books of reference. In preparin>^- for them, one pupil should 
be required to obtain from certain sources indicated by the 
teacher the information bearing- upon some particular part of 
the subject, and other phases of it may be assigned to differ- 
ent other pupils. These composite lessons may be made 
extremely interesting by means of skilfully conducted recita- 
tions, the purpose of which is to combine into an orderly 
whole the contributions of the several pupils. The text- 
book matter may afterwards be studied for the purposes of 
review, and of organizing many lessons into continuous and 
logical unity. 

84:. Stencil Maps. — Every teacher of geography should 
know how to prepare stencil maps and sketches of various 
kinds. These may be bought from almost any educational 
publishing house. Catalogues may be obtained giving lists 
of stencil outlines of maps, plants, animals, insects, portraits, 
etc., and their prices. These stencils consist of sheets of thin 
paper in which minute perforations represent the correct 
outlines and the necessary details of the objects to ba repre- 
sented. They are of a size suitable for blackboard drawings. 
To use them, it is necessary only to place them against a 
blackboard and go over them gently with a felt black- 
board rubber that has been rubbed full of crayon dust. 
Upon removing the stencil, it will be found that a faint out- 
line of the drawing has been transferred to the board. This 
may then be lined in with crayon of any required color, and 
such other details may be added as the drawing requires. 

Of course, if the teacher is skilful in drawing, these sten- 
cils will not be required; but the fact is that few teachers 
are possessed of this very valuable accomplishment. 

It is stated above that these stencils may be bought, but 
better still, each teacher may make them himself or have his 
pupils make them. A satisfactory method of doing so is as 
follows: 

With a lead pencil make on a sheet of thin paper an out- 
line sketch of the map or other object of which a stencil is 



102 



PEDAGOGICvS OF GEOGRAPHY. 



required. Then place a couple of sheets of thin paper under 
this, and pin the whole together at the corners. Put a fine 
needle into a sewing machine and follow the traced lines of 
the drawing. In order to prevent a burr from forming on 
the under side of the pierced holes, the sheets should be 
placed upon a piece of manila paper while the perforations 
are made. These stencils should be preserved; for they 
may be used a great many times, and they will be found 
extremely useful, not in teaching geography only, but in 
connection with nearly every other school subject. Indeed, 
the teacher gifted with resourcefulness will continually find 
the means of devising helpful appliances for giving interest 
and vividness to his work. 

85. Pictured Comparisons. — The graphic representa- 
tion of facts, relations, processes, and principles, as shown in 




U.S. 



Elsewhere. 
Fig. 10. 



U. S. 



Elsewhere. 



Figs. 10, 11, 12, 13, and 14, has come to be indispensable in 
the best phases of modern teaching. What teacher now 
could expect to succeed in teaching grammar, for example, 




Elsewhere. U. S. Elsewhere. 

Fig. 11. 



if he were debarred from using a good scheme of diagrams ? 
Could any one teach physics, astronomy, chemistry, botany, 
or any other of the natural sciences without the aid of 
graphic representation ? The same kind of help is required 



§5 



pedagcXjICS of geography. 



1U3 



in geography. As has been remarked, statistics relating to 
many subjects are of great importance, especially if it be 
desired to introduce the principles of cause and effect, and 



'■*T r^i ^^ 11^ 

Elbe^\he^e L s 

Fig. 1-,'. 





U & 



U. S. Elsewhere. 



considerations involving comparison. Our late textbooks 
are beginning to make much use of the graphic method of 
representation, and it is easy to see that this is a tendency in 




Elsewhere 



the right direction; for any one can understand how much 
more forcibly such truths as the above can be shown by 
pictures than if they are merely stated in words. 

It is not necessary that a teacher should be able to draw 
skilfully in order to use the graphic method. Stencils of 
figures in outline are easily made or obtained, and they are 
available ever afterwards. Even if a teacher has no skill 
whatever in drawing he is almost certain to have in his class 
one or more pupils that can do well what may be required. 

The accompanying cuts are only a few of the innumerable 
illustrations that may be used advantageously in this work. 
They all represent activities in which those of the United 
States are compared with the rest of the world ; but equally 
instructive would be those cases in which the reverse is true. 

The illustrations above were suggested by cuts of a similar 
kind in "The Natural Advanced Geography " of Redway and 
Hinman, a late and very admirable work published by the 
American Book Company of New York. 



104 PEDAGOGICS OF GEOGRAPHY. § d 

86. Graphic Geoiuetrical Forms. — A method of 
illustration requiring- no skill whatever in drawing is that 
involving the use of certain geometrical forms. Among the 
most suitable of these are the square, the rectangle, the cir- 
cle, and rectangular solids, variously grouped and subdivided. 
A method used very extensively in European schools consists 
in parallel straight lines of unequal length. These furnish a 
very convenient means of showing comparative heights and 
distances, as well as areas, products, wealth, commerce, etc. 
The following is an example : 

J{// Jid il roads. 



^^tKtKM Atlantic Ocean and Cr^ii If of Mexico. 

immmtm Great Lakes, 

^mm Mississip'pi and its Tributaries. 

■■ Canals. 

mm J^aci fie Ocean. 

Comparative Transportation of the Commerce of the United States. 
Fig. 14. 

To illustrate further the manner of using these graphic 
devices, let us suppose that the area of Texas is to be compared 
with the areas of certain European countries. If these areas 
are to be compared by //ucs of imequal length, we know that 
the lines mi;st vary in length as the (rrcas ; but if we wish to 
represent comparative areas by surfaces, as, for example, by 
squares, then we must make their sides proportional to the 
square roots of those areas. Moreover, if so/ids, such as 
cubes, were used, their edges must be proportional to the 
cube roots of the areas. In case these dimensions are not 
great enough or small enough, we may multiply or divide 
them by any suitable number, provided we use the same 
multiplier or divisor for all of the dimensions. 

A very good way to prepare for the actual representation 
is to construct a table beforehand, and require the pupils to 
make all the calculations. In such tables, the areas of coun- 
tries should be given in square miles to the nearest thousand. 



S 



PEDAGOGICS OF GEOGRAPHY 



lO.j 



Such a table, for representing" graphically the areas of the 
countries named in it, is shown below. The accompanying- 
cut is somewhat reduced from the dimensions of the drawing; 
indicated in the table. 



Covintrv. 


Area in 
square 
miles. 


Area 
1,000. 


.Side (if Square. 


Texas 


266,000 
210,000 
207,000 
192,000 
126,000 

121,000 
116,000 

111,000 


266 

210 
207 
192 
126 

121 
116 

HI 


14/266 = 16.3 H- 4 = 4.08 
^4/210 =: 14.5-4 = 3.63 
i|/207 = 14.4 --4 = 3.60 
1^/192 = 13.9-^4 = 3.50 
^|/T26 = 11.2 --4 = 2.80 

1V'121 = 11.0-4 = 2.75 
14/116 = 10.8H-4 = 2.70 

^4/111 = 10.5H-4 = 2.63 


German Empire 

h ranee 

Spain 


Hunijary 


Great Britain and Ire- 
land 


Austria 


Italy, Sicily, and Sar- 
dinia 





. dirjIKUl >J 



-Spu iji 



_Iii: Britain 



.Ualij 



Fig. l.j. 



•106 PEDAGOGICS OF GEOGRAPHY. § 5 

87. Clay, Sand, or Pasteboard for Modeling. — Clay 
or sand modeling has come to be regarded by the best 
authorities as indispensable in the earliest geographical 
teaching. In every classroom where the first lessons in 
geography are given, there should be a modeling board 
about 48 in.x CO in., and this should have around it an edge 
raised about H inches. This board may be attached by 
hinges to a table, and in some convenient receptacle there 
should be a generous supply of sand. The sand may be 
obtained from any foundry, or ordinary beach or builder's 
sand may be used, although it is not quite so good. Mois- 
tened occasionally, and kept covered with a cloth, it is always 
ready for use. 

Each pupil should be provided with a shallow pan 
12 in. X 20 in., as well as with a piece of thin wood or metal 
similar in shape to a spatula or a paper knife. 

For more advanced pupils, modeling clay or putty may 
be substituted for sand. A supply of either of these, if 
properly cared for, will last a long time, and their cost is 
inconsiderable. The work of modeling has lately received 
so great an impetus in our schools that many of our large 
cities are now furnishing clay for the use of pupils, just as 
they supply books and stationery. In the town and country 
schools this is not done, biit a teacher with proper enter- 
prise and enthusiasm in his work will find a remedy for the 
omission. 

When maps showing contours representing elevations can 
be obtained, very, much more accurate models may be made 
by using pasteboard of uniform thickness. Since contour 
lines usually represent elevations by differences of 100 feet, 
one layer of pasteboard may be taken as representing this 
height. Before cutting the pasteboard, each contour Ime 
should be sketched in proper scale on its surface, and the 
several pieces may then be cut and firmly pasted on one 
another. The result will show for each elevation a series of 
terraces, which, indeed, are not true to the fact, but this is 
a matter of slight consequence. It is always possible to 
obviate this difficulty by filling in the terraces with plaster 



§ 5 PEDAGOGICS OF GEOGRAPHY. lOT 

or other suitable material. From these models casts may be 
made, and these in turn may be used as molds from which 
plaster casts may be obtained. Of course, this elaborate 
work, with pasteboard to show relief forms with approxi- 
mate exactness, is suitabL> only for advanced pupils that 
have aptitude and taste for it, but the study of their work 
by other pupils is in a very higli degree beneficial. 

88. Maps of the Governiiieiit Survey. — Every teacher 
should be provided with specimens of the maps that are 
made by the United States Geological Survey. They are 
very complete, showing on larg-e scales every variety of 
topographical and geological features — every stream, road, 
lake, swamp, hill, mountain, church, schoolhouse, village, 
etc. The object of the government is ultimately to have a 
complete and minute survey of all the states and territories 
that make up the vast possessions of the country. At pres- 
ent, somewhat more than one-fifth of this work has been 
accomplished, but something- has been done in every state 
and territory, and in a few of the more populous, the survey 
and mapping have been nearly or quite finished. 

These maps are perfect aids in teaching home geography. 
With them, the teacher can get for his rude blackboard maps 
every fact required to give interest to his teaching. The 
wonderful perfection of these maps will surprise the teacher, 
and they furnish the means of indefinite improvement in the 
teaching of geography. 

89. Description of tlie Topographic Map of the 
United States. — The waiter is convinced that it will be help- 
ful to the teacher of geography to give him exact informa- 
tion about the maps of the United States Geological Survey, 
and to let him know exactly how they are to be obtained. 
The following description is therefore copied from the back 
of one of these maps : 

The United States Geological Survey is making a topographic map 
of the United States. Tliis work has been in progress since 1882, and 
about one-fifth of the area of the country, including Alaska, has been 
mapped. The mapped areas arc widely scattered, nearly every state 



108 PEDAGOGICS OF GEOGRAPHY. § o 

being represented, as shown on the progress maji accompanying each 
annual report of the Director. 

This great map is being published in atlas sheets of convenient size, 
which are bounded by parallels and meridians. The four-cornered 
division of land, corresponding to an atlas sheet, is called a qitad- 
raiigle. 

The sheets are approximately of the same size: the paper dimen- 
sions are 21| by 18} inches; the map occupies about Yi\ inches in 
height and 11), to 16 inches in width, the latter varying with latitude. 
Three scales, however, are employed. The largest scale is 1 : 62,500, 
or very nearly one mile to an inch ; that is, one linear mile on the 
ground is represented by one linear inch on the map. This scale is 
u.sed for the thickly settled or industrially important parts of the coun- 
try. For the greater part of the country an intermediate scale of 
1 : 135,000, or about two miles to one inch, is employed. A third and 
still smaller scale of 1 : 250,000, or about four mil«s to one inch, has 
been used for the desert regions of the far West. A few special maps 
on larger scales are made of limited areas in mining districts. The 
sheets on the largest scale cover 15' of latitude by 15' of longitude; 
those on the intermediate scale, 30' of latitude by 30' of longitude ; and 
those on the smallest scale, 1° of latitude by 1° of longitude. 

The sheets are sold at five cents each when fewer than 100 copies 
are purchased, but when they are ordered in lots of 100 or more copies, 
whether of the same sheet or different sheets, the price is two cents 
each. 

■;:- ■::- * * * * Applications for the separate topographic maps or for 
folios of the Geologic Atlas, accompanied by the cash or by post-office 
money order (not jjostage stamps), should be addressed to 

The Director, 
Iniited States Geological Survey, 

Washington, D. C. 



MATTER A:XD METHOD IX GEOaEAPHY. 

90. The Important and tlie Trivial. — Soine one has 
defined a weed as " a plant out of place. " For example, if a 
stalk of maize should appear in a field of wheat, it would be 
a mere weed. It is an intruder; is part of no g-eneral scheme; 
its presence is not helpftil but hiu'tful ; the natural prompting 
is to uproot it and cast it aside. So, also, in education, it 
does not follow that, because anything- happens to be true, it 



§5 PEDAGOGICvS OF GK()(;RAPHY. Kid 

has value and should therefore be taught. "A faet, " says 
SchelHng-j '-is in itself nothing." Unless it is a necessary 
part of a coordinated whole, — is a link in a chain of 
sequence, — it should usually have no consideration. 
"United we stand, divided we fall" is an axiom in science 
as well as in politics. There is no virtue or value in isola- 
tion. For the teacher to have in his mind a distinct general 
scheme of the subject he is teaching; to keep this scheme in 
constant view while developing its details from day to day 
and from week to week; to present to his class all these 
details in proper relation and order, guarding always against 
irrelevancies, until he has put his pupils in possession of the 
same clear, sharply outlined conception of the subject that 
he himself has, is not easy, but it is indispensable to the best 
results in teaching. A great poet seeking the highest eiTect 
must know how to discriminate between the important and 
the trivial, between that which is relevant and essential to 
the effect he would produce and that which adds to it nothing. 
In this respect his work resembles that of the teacher, but it 
is perhaps less difhcult. The teacher is continually impor- 
tuned to notice and emphasize facts that have no other claim 
on his attention than that they are curious, striking, fantas- 
tic, or wonderful. And herein lies the chief fault in the 
teaching of geography; its continuity is broken and its sci- 
entific character is lost by an almost unavoidable instinct 
to make tlie geographical story like that told by Othello, 
wherein he spoke 

* * of antres vast and deserts idle, 

Rough quarries, rocks and hills whose heads toncli heaven. 

And of the Cannibals that each other eat, 
The Anthropophagi and men whose heads 
Do grow beneath their shoulders. 

This kind of thing is very interesting, but it is not in any 
proper sense geography. 

91, Sailoi' Geog-rapliy. — The report of the Committee 
of Fifteen, by describing what is called "sailor geography," 
illustrates what is said just above. 



liU PEDAGOGICS OF GEOGRAPHY. § 5 

At first there prevailed what miglit be named sailor geography. 
The pupil was compelled to memorize all the (names of) capes and 
headlands, bays and harbors, mouths of rivers, islands, sounds, and 
straits around the world. He enlivened this, to some extent, by brief 
mention of the curiosities and oddities in the way of cataracts, water- 
gaps, caves ("antres" of Shakespeare), strange animals, public 
buildings, picturesque costumes, national exaggerations, and such 
matte7-s as wojild furnish good i hemes for sailors' yarns. Little or 
nothing was taught to give unity to the isolated details furnished in 
endless number. 

In many of our schools there is yet a strong- leaning 
towards tmdtily emphasizing the curious and abnormal 
thing's that are found in the various parts of the earth. This 
is perhaps accounted for by the fact that in the process of 
the development of the race we have not yet reached the 
deliberative, philosophical period when principles and laws 
yield more pleasure than the curious and the incidental; 
when the sensational, gossiping-, scandal- spreading journal 
is more widely read and enjoyed than the cleanly edited 
philosophical paper. Our teaching is perhaps as g-ood as 
the people expect or deserve, but that is not the inain point 
to consider. If we are to outgrow and put aside the things 
that belong to a rudimentary civilization; if, leaving the 
"yellow" journal and all that it signifies, we are to grow 
constantly towards that which is higher and nobler, into 
wider and more refined sentiments and sympathies, we must 
have something better than sailor geography. And this 
something better we must get from our teachers more than 
from any or even from all other influences. 

93. The "Capital-and-Botindary" Geograpliy. — Fol- 
lowing the period of sailor geography, there came a phase of 
the subject that might be called the " capital-and -boundary " 
development. If, in addition to the miscellaneous details 
that were dwelt upon in sailor geography, a pupil could bound 
and give the capital and mention one or two important cities, 
his knowledge of geography was regarded as lacking nothing 
in completeness. But there came Avith this advance some- 
thing that led rapidly to a higher conception of the best 



§5 PEL)AGO(tIL\S OF (tEOCtRAPHY. Ill 

g-eog'raphicul teaching. This was map-drawing. The neces- 
sity of studying' watersheds and mountains and drainage was 
speedily followed by attention to industrial centers with their 
natural resources and their manufactured products, to routes 
of commerce, and to the causes, conditions, and directions of 
development. Inevitably, from all these matters there would 
come and did come a distinct recognition of cause and effect 
as the most important principle regulating both the choice of 
matter and the methods of instruction. Or, as it is phrased 
in the important report already quoted from: 

Instruction in geography is growing better by the constant introduc- 
tion of new devices to make plain and intelligible the determining 
influence of physical causes in producing the elements of difference and 
the counter-process of industry and commerce by which each difference 
is rendered of use to the whole world, and each locality made a partici- 
pator in the productions of all. 

But this capital-and-boundary method is still widely fol- 
lowed by teachers that have come down to us from the old 
regime, as well as by many younger teachers who cling to the 
methods followed in their own education. Of these two 
classes the former is almost hopelessly beyond the reach of 
any influence for change in the direction of growth and 
improvement, but with the latter this is not so much the case. 
For there is a contagion for betterment in nearly all the edu- 
cational influences about us; and these influences are practi- 
cally irresistible by teachers that have youth and intelligence, 
and are therefore capable of growth. 

93. Need for Discriminating' Among* tlie Facts of a 
Science. — If there is a subject in which it is more dil^cult 
than in any other to discriminate between the important, the 
essential, and that whicli may be passed by, it is geography. 
As has been remarked, the field of geography is a vast 
one, covering in some measure nearly all the natural sciences. 
The chief difficulty lies in organizing from this enormous 
detail of loosely connected facts a coherent whole of which 
all the elements are essential to its scientific imity and com- 
pleteness. There must be nothing lacking and nothing* 



112 PEDAGCXilCS OF (xEUGRAl'll V. 



i5 ■> 



redundaut. vScarcely any fact that can be construed as 
belonging to the domain of geography is without interest to 
somebody at some time in his life, but it does not by any 
means follow that it is a fact needing to be for that reason 
introduced into a textbook of geography. A gazetteer or a 
guide book would perhaps be deficient without it; but, in a 
geography for school use, it would be irrelevant and imper- 
tinent. For example, it might be an advantage to know the 
exact latitude and longitude of every place of any importance 
in the world, to know the air-line distance from each city 
to every other city, or to carry in the mind all the important 
figures of each census made at various times; but no one 
that studies geography of this kind need hope to get from 
the study, however prolonged, any knowledge of it as a scien- 
tific unity. The study of isolated facts is one thing; the 
mastery of related facts organized into a science is quite 
another. 

To illustrate, the following are taken at random from a 
textbook that was once very much used: 

Jh-adjo) d has colleges for Baptists, Independents, and Wesleyans, 
and is the principal seat for the worsted-yarn manufacture. 
. Dessau is a neat little town on the Mulde. 
Bernbiirg is a small industrious town on the .Saale. 
Newbury is celebrated for its serges and shalloons. 
Szej^eef/ft, on the Theiss, is a place of great trade. 

The book contains thousands of such statements; these, 
however, will sufficiently illustrate. The fact that they 
are put into a textbook implies that they are regarded as 
of sufficient importance to be studied, but of what value 
can it be to know that one little town is " neat " and another 
is "industrious," and that a third produces "shalloons".? 
These facts may be permitted in a gazetteer, but they are 
very much out of place in a geography for school use. 

94. Evolution of Textbooks. — It is not many decades 
since all textbooks consisted of an undigested mass of facts, 
with no suspicion of science or logic or orderly sequence in 
their matter or arrangement. Maps were of little use except 



g 5 PEDAGOGICS OF GEOGRAPHY. 113 

for playing "hide-and-seek" among geographical names; 
no hint could be found that great mountain ranges, rivers, 
ocean currents, or coast indentation have any influence in 
shaping national activity, development, or history. 

But little by little, improvements in textbooks have gone 
on, until now we have in this country some that are admi- 
rable — textbooks in which the subject appears in the aspect 
of a science. In some of these works, facts are subordi- 
nated to the principles and to the laws that they illustrate; 
effects are traced to their causes, and at every step it is the %vliy 
not the zvJiat that is emphasized. The student of the subject 
so presented is compelled to think, to reason, and, in a meas- 
ure, to philosophize. The result of his study is a nucleus of 
laws and principles that gathers to itself, from year to year, 
thousands of facts; and these facts are easily assimilated 
and remembered because they illustrate these laws and prin- 
ciples. The advantage that comes from the application of 
the laws of the association of ideas in teaching is seized in 
every possible manner, and the correlations of geography 
with other subjects are constantly utilized. It would of 
course be invidious to specif}^ in this Paper any of the text- 
books referred to, and it is really not important that this 
should be done; for any teacher, after a brief search, can 
easily find the best for his particular purpose. 

This process of evolution in textbooks will imdoubtedly 
continue and keep pace with the wonderful development of 
the earth's resources that has been so marked in the last two 
or three decades. The student should note, too, that this 
growth and progress prevent every presentation of the 
science from being for any great length of time satisfactory 
in the classroom. Geography, more than any other subject, 
very quickly gets out of date. 

95. Some Points to Be Observed iu Teacliing 
Geography. — Whether the textbook used be old or recent, 
good or bad, there are certain general principles of teaching 
that may be kept in mind with manifest advantage. 

1. Teach map-sketching rather than map-drawing. 



114 PEDAGOGICS OF GEOGRAPHY. § 5 

Considered as an aid in geographical teaching, elaborate map- 
drawing, for the time and labor involved, yields a very slight 
return. The rapid and general sketch is, however, indispen- 
sable. It shonld be employed constantly — in history as well 
as in geography. 

2. Never teach names for their geographical value 
alone, for they have none. A name in geography should be 
a nucleus or center about which many related ideas cluster. 
The same may be said of facts. To teach a class, for exam- 
ple, that Chicago is a city of very rapid growth, would be 
a waste of time and words; but, if the conditions and 
caiises of such development are pointed out, the pupil will 
not only remember the fact, but he will have a principle to 
guide him in investigating the same subject with respect to 
other cities. In teaching isolated facts, you require him 
to use his memory alone; in referring to causes and conse- 
quences, you appeal to his judginent, his reason, his logical 
faculties in general, as well as to his memory. 

3. In geography the object should not be to cover a 
great expanse, but to do the work very thoroughly. vSome 
one advises that if you have ten minutes in which to solve 
an example, you should spend the first eight minutes in 
thinking about it and planning the solution. So in geogra- 
phy — spend less time in learning new facts than in consider- 
ing the relations of the old and in correlating them with the 
new. Hence, 

4. Proceed by the method of constant comparison. It 
is vastly better to know that the area of California is about 
three and one-half times as great as that of Pennsylvania or 
Cuba than it is to know that it has an area of a little more 
than 158,000 square miles. 

5. Be sure that you have definite standards of compari- 
son. Of these there should be, 

((?) A standard of Icngtli — the mile, and its subdivisions. 

{b) A standard of area — the square mile and the acre; 
also a larger standard, as the area of Kansas. 

[c) A standard of arc uieasurcntent — the degree and its 
subdivisions. 



§0 PEDAGOGICS OF GEOGRAPHY. 115 

(<•/) A standard of altitude. In estimating mountain 
heights, the standard is feet ; but for great sea depths and lofty 
peaks use if possible a mountain that the pupils have seen. 

{e) A standard of population to the square mile. Thus, 
in 1900 the population of the United States and territo- 
ries, including Alaska, is about 22 to the square mile; so 
that each man, woman, and child might have a farm of 
nearly 30 acres. When the pupil learns that China has 
about 230, and Belgium more than 530, to the square mile, 
he has material for many valuable reflections upon the sub- 
ject of man's distribution and future upon the earth. 

G. Teach physical and political geography together. The 
separation is arbitrary and has only a theoretical value. 

7. Develop constantly the causes and consequences of 
geographical facts. Some illustrations of this are foimd in 
an earlier paragraph of this Paper. 

8. The deductive method has many excellent applications 
in teaching geography. For example, here is a city on the 
Pacific coast of the United vStates. The warm Japan current 
strikes the coast and is accompanied by currents of warm air 
heavily laden with vapor. During the hot summer months 
the heated air from the mountains that extend north and 
south blows seaward ; in the winter months the w"ind is in 
the opposite direction. What should you expect the result 
to be with reference to rainfall and seasons, and what effect 
would these varied circumstances have upon the healthfi;l- 
ness, the industries, the commerce, and the development of 
that city and its surroundings ? 

9. Never require pupils to commit geographical facts to 
memory. If taught correctly, children cannot avoid remem- 
bering. If they do forget the facts, they will assuredly 
remember the principles, and with these in their minds they 
will be geographical students for life. 

9G. Map Reading.— An essential object to be attained 
in the teaching of geography is the ready and intelligent 
reading of maps. Even more necessary to the true mastery 
of the science is the establishment of a habitual tendency to 



110 PEDAGOGICS OF GEOGRAPHY. § 5 

find in the map a means of sharply conceivini;- tlie reality for 
which the map stands. In mathematics we quickly get to 
dealing with quantity and number in the abstract. Very 
soon many concrete objects are adequately represented to 
the mind by Arabic numbers or algebraic symbols ; but in 
geography we must constantly make the transfer from the 
map that represents to the symbolized reality. If we fail 
to do this, the great round earth, with its myriad varieties 
'of structure and feature, of life and motion, becomes noth- 
ing more than the flat surface of a paper map. The sight 
of the map should always be only preliminary to an aerial 
excursion in imagination, during which we pass over broad 
plains and real mountains, and trace the. rivers for hundreds 
or thousands of miles down long slopes and past busy, smoky 
cities, and quiet villages and farms, until they pour their 
waters, reenforced by hundreds of lateral streamlets, into 
the broad bosom of bay or ocean. If we fail to do this, we 
are studying, not geography, but chartography, we are 
dealing with shadows, not realities. The pupil that has been 
thus trained in vividly conceiving the reality from the hints 
furnished by the map, will indeed be surprised at the vast 
scale of that reality when he comes to see it, as compared 
with his previous conception of it; but he will not, as is the 
case with one that has been allowed to forget that the map 
is only a symbol, be convinced of the utter futility of the 
study of geography as a means of making him acquainted 
with the world before he has actually seen it. 

Hence, the reading of maps and globes is the crucial test 
of geographical teaching. When you meet the name of a 
river, a city, a mountain, do you call up the image of the 
map and rest with that, or does the mind, guided by what 
the map has suggested, fly away over mountains and plains 
and oceans and look down as if from a balloon upon the pres- 
ent reality? If you do the latter, you have studied geography 
to valuable purpose; otherwise, your study has been utterly 
barren. You have been learning mere words and lines and 
colors. The procedure is identical in futility with the study 
of words without reference to their meaning. 



§ 5 PEDAGOGICS OF GEOGRAPHY. 117 

97. Importance of Wall Mai)s. — Schools should be 
supplied with wall maps. Of these there are many of vary- 
ing degrees of usefulness for practical work in the classroom. 
Some of the essential conditions of value in wall maps are 
the following: 

1. The coloring should not be brilliant, nor should con- 
trasts be striking. Anything of this kind is calculated to 
divert the mind from concentrated and continuous attention 
to the matters that a map should show. It is well known 
that children are easily attracted by vivid coloring, and many 
maps are made more for the purpose of pleasing the eye and 
selling readily, than for instructing the mind. The best 
maps of the government are almost devoid of color, and the 
chartographers of Germany, where, confessedly, the most 
excellent of the world's maps are made, and whose people 
have a weakness for striking color effects, avoid this common 
fault in map-making. 

2. Wall maps should show general features, but not 
minute details. A map for reference and a map for teaching 
should differ very decidedly. The confusion of detail in a 
reference map renders it almost useless for purposes of 
instruction. A wall map should be constructed primarily 
to show physical features, — slopes, drainage, relief, con- 
tours, — but towns and cities and strongly emphasized politi- 
cal boundaries and divisions belong in the reference 
maps. They should reveal strongly and distinctly the phi- 
losophy of geography, not the temporary changes that are 
the result of man's political and industrial activity. A wall 
map should be rich in the suggestion of geographical cause 
and effect. 

A late writer on this subject says that such expressions as 
the following are of frequent occurrence in German and 
Swiss works on pedagogics: 

The map, the truest representation of the earth's surface, in which 
explorers have recorded their observations, is the chief means of geo- 
graphical instruction. 

We must see to it that the pupil gives his interpretation to the char- 
tographic signs ; that he translates into and out of the map the correct 



118 PEDAGOGICS OF GEOGRAPHY. g 5 

geographical relations. Map reading is the foundation of geographical 
instruction in the work that follows home geography [/leiiiiaikunde). 
It was -prepared for in the heimatkunde ; here it must be broadened 
and deepened. 

98. The Map in Recitation. — Even with the advantage 
of having the very best of wall maps, the teacher may fail to 
obtain good results by not using them properl}'. Success 
need not be expected by the old method of requiring pupils 
to look up and memorize map questions, nor by asking them 
to recite verbatim a vast mass of descriptive text. The 
knowledge that is merely pigeonholed in the memory, and 
has been worked over by no other faculty, is usually more of 
a hindrance than a help in practical life. It is the logical 
and orderly reading of what is revealed by the map, and this 
tmder the teacher's guidance, the tracing of causes and con- 
sequences that lie implicitly among those facts — the correla- 
ting and coordinating of facts and principles — it is all of tins 
that is necessary to the highest siiccess. 

Every recitation period should be divided into two parts; 
the first should be employed in a review of the lesson of the 
preceding day, — emphasizing it and unifying it with other 
parts of the general subject, — the second in teaching- a new 
lesson. This lesson should not be assigned as something to 
be studied, memorized, and recited, but rather it should be 
developed somewhat after the investigation or laboratory 
method. In this process the teacher must be the director 
and guide — himself the most alert of the learners. If the 
work has been well done, the pupils will carry away from the 
classroom an impression so vivid, so inspiring, so fi;ll of 
profitable suggestion, that all subsequent study of geography 
will be better for it. They will furnish an imperishable 
picture of the region studied; and with such a picture in his 
mind, the pupil will ever thereafter feel an irresistible craving 
for more knowledge to fill in the details of his picture. In 
this impulse to acquisition that good lessons furnish, lies 
their chief value and the best argument for the teacher's 
personal direction while they are being developed. 

It must not be inferred that the ordinary textbook on 



§ 5 PEDAGOGICS OF GEOGRAPHY. 119 

geography is to be banished from the ehiss work. On the 
contrary, every pupil should have one. It will be found that 
a lesson under the supervision of the teacher, in the manner 
described above, will furnish an impetus that will send each 
pupil to his textbook with his eyesight and mind clarified to 
see and iinderstand as never before. He will go there for 
material to complete his picture of the reality, and at the 
next lesson he should be required in the review to demon- 
strate that he has really added to it, and that his additions 
are important and relevant. While the wall map and the 
globe are the foundation of geographical teaching, the text- 
book is their most useful adjunct. The best work requires 
the .second as well as the first. 

99. A Model Jjessoii. — The following lesson is intended 
to suggest the way in which, by the method of question and 
answ^er, a lesson from the wall map should be conducted. 
It is the report of a lesson actually listened to by an intelli- 
gent observer among the schools of Central Europe. The 
writer says: 

Let us suppose that the lesson is on the relief map of Europe. In 
some previous lesson the pupil has read from the wall map the triangu- 
lar form of the continental mass of Europe, and has noted its west, 
east, southwest, and southeast angles. It is to the relief of this con- 
tinental triangle that his attention is now directed. 

Teacher. Tell me in what part of continental Europe you find the 
lowland represented, and in what part the highland. 

Pupu.. The lowland is in the northeast; the highland is in the 
soiithwest. 

T. Look at the map again and tell me whether it is all lowland in 
the northeast. 

P. Some small highlands are represented there. 

T. Is the southwest all highland ? 

P. There are some small lowlands among the highlands of the 
southwest. 

T. State what you have learned from the map. 

P. Northeast continental Europe is mostly lowland. Southwest 
continental Europe is mostly highland. 

T. In what direction must I draw a line to separate the lowland 
from the highland ? 

P. From northwest to southeast. 



120 PEDAGOGICS OF GEOGRAPHY. § 5 

T. Some one may point to the northwest part of the highland. What 
river's mouth is just above it ? 

P. The Rhine. 

T. Some one may point to the southeast part of tlie highland. What 
river's mouth is just above it ? 

P. The Danube. 

T. Between what points, then, may my line dividing the lowland 
from the highland extend ? 

P. From the mouth of the river Rhine southeast to the mouth 
of the river Danube. 

T. This line is called the mountain diagonal of Europe. You may 
state how the lowland part of continental Europe is separated from the 
highland part. 

P. Lowland continental Europe is separated from highland con- 
tinental Europe by the r^ountain diagonal. It is a line drawn from the 
mouth of the Rhine to the mouth of the Danube. Northeast of this 
line the surface is mostly lowland ; southwest, mostly highland. 

T. We will now attend to the highland part of continental Europe. 
In what direction must I draw a line from the northwest end of the 
mountain diagonal to clear the highland on the west side ? 

P. Southwest. 

T. In what direction to reach the southeast end of the mountain 
diagonal ? 

P. East. 

T. What, then, is the form of highland continental Europe, and 
what are its bounding lines ? 

P. Highland continental Europe has the form of a triangle ; its 
boundaries are the mountain diagonal on the northeast side, a line 
drawn southwest from the mouth of the Rhine, and a line drawn east 
to the mouth of the Danube. 

T. Look at the map and tell mc which part of the highland is 
highest. 

P. The south. 

T. Of what does this highest part consist ? 

P. Mountain chains. 

T. What name do you give to several nunmtain chains extending 
in one general direction ? 

P. A mountain system. 

T. This mountain system is called the Alj^s. You may state what 
you have learned about the southern part of the highlands. 

P. The highest part of the highland of continental Europe is in the 
south. It consists of many mountain chains, forming the mountain 
system of the Alps. 

T. Look at the map and tell me how you see the rest of the highland 
represented. 



§ 5 PEDAGOGICS OF GEOGRAPHY. 121 

P. Broad spaces bounded by mountain chains. 

T. These broad spaces ai-e plateaus and elevated river basins. How 
do they compare with the Alps as to height ? 

P. They are lower. 

T. In what direction from the Alps do they lie ? 

P. West, north, and east. 

T. You told me that there were several small lowlands in different 
parts of the highland. See whether there are any of these between the 
Alps and the plateaus and river basins, and to what rivers they belong. 

P. There is one southwest of the Alps and another in the east. The 
southwest lowland belongs to the Rhone and the east lowland to the 
Danube. 

T. Look at the plateau region north of the central part of the Alps 
and see whether it is joined to them or separated from them. 

P. It is joined to the Alps. 

T. This region of plateaus, elevated river basins, and mountains is 
called the middle mountain and plateau system of Europe. The word 
juiddlc has reference to its elevation, which is not so high as the Alps 
and not so low as some other mountains, etc. of continental Europe 
that lie outside of this region. You may state what you have learned 
about this part of the highland. 

P. A region of plateaus, elevated river basins, and mountains lies 
west, north, and east of the Alps. It is called the middle mountain 
and plateau system of Europe. It is separated from the Alps in the 
west by the valley of the Rhone river, in the east by the valley of the 
Danube, and is joined to the Alps in their center on the north side. 

100, Siiniiiiary of Xiessons. — Before any of these les- 
sons are undertaken, the teacher should prepare a careful 
summary of what he proposes to develop. He should do 
this with studied thoroughness, and should plan also the 
substance and the order of his questions. There is a pretty 
general impression among teachers that the superiority of 
their knowledge above that possessed by pupils is suf- 
ficient warrant for neglecting preparation for lessons. No 
worse error could possibly be promulgated. Even teachers 
of the longest experience and the highest attainments can- 
not afford to be neglectful of this first duty of a teacher. 

Stippose the le.sson is to be an exercise in reading the con- 
tour of Farther India. The following, taken from an article 
by Director Heiland, of the Weimar Seminary, will show 
such a summarv of an intended lesson. 



122 PEDAGOGICvS OF GEOGRAPHY. § 5 

Farther India has the form of a triangle ; its base line is the Tropic 
of Cancer, between 90° and 110*^ east longitude from Greenwich, or 
between the Ganges-Brahmaputra delta and the meridian of Hainan 
island. The vertex is Cape Romania, in 1}° north latitude, on 
the same meridian as Cape Chelyuskin, the northernmost point of 
Asia. Base is to height as 3 to 4. Length from north to south is 
(33^° — 1^°) X 60, or 1,335 geographical miles. Length of base line is 
(110' — 90") X 55, or 1,100 geographical miles. Direction of west coast 
is from northwest to southeast, interrupted by the gulf of Martaban. 
It has thi-ee natural divisions: (1) from Ganges-Brahmaputra delta to 
the Irawadi; (2) to the angle of Malacca; (3) to Cape Romania. Direc- 
tion of (1) and (3) west-northwest to south-southeast. Lengths equal. 

The student will of course understand that this kind of 
work belongs in later geogTaphical study, bttt it should by 
all means be found there. An exact mental picture of any 
cotmtry can be attained in no other way than by some such 
orderly examination. 

101. Ciinse and Effect in Teacliiiig' Geog-rapliy. 

It has already been stated that there is little of educational 
value in isolated facts. Indeed, one of the conditions 
essential to the organization of facts into a unified and 
coherent science is that these facts shall be related among 
themselves. Now, there are many bonds of relationship 
possible among facts, but the strongest of these bonds is that 
of cause and effect; and of all the various sciences, none is so 
strongly permeated by this principle as is geography. The 
play of the forces of nature is all in harmony with the laws 
of cause and effect, and the activities of men and nations 
cannot be interpreted or anticipated without constant refer- 
ence to them. Geography, therefore, .should be the most 
interesting of all sciences and the one most skilfully taught, 
and it might be, if teachers would avail themselves of the 
natural and logical method that the subject itself .suggests. 
It is in this that the schools of Central Europe are giving 
an instrtictive lesson on pedagogics to the rest of the educa- 
tional world. 

The following description of a lesson in a German school, 
durino- which the teacher observed the cause-and-cffect 



§ 5 PEDAGOGICS OF GEOGRAPHY. 123 

method, will enable the student to understand the impor- 
tance of this principle: 

A lesson was listened to in a German school where seventy boys sat 
together like sardines in a box. The teacher had nothing better than 
a medium-sized wall map made by himself. His mode of marking 
elevations was very simple and comprehensive — one that is well worth 
imitating. With pencil or pen he shaded the map by means of lines 
crossing one another at various angles. Thus he represented the 
topography of a country in a remarkably accurate manner, and this 
easy method enabled his pupils to judge at a glance as to the height of 
the land. They saw icIiy certain r/'c't-rs tool: such a/ui such a course 
and no other; ix'hy certain countries locre cold, others tvarni. They 
saw why a river was navigable or not according to the abruptness of 
the slope; 7uhy certain rivers, flowing from great heights, had a 
straighter course than rivers that had a more gradual slope or mean- 
dered through a plain ; \ohy certain lands are blessed uith mild cli- 
mates when sheltered on the north side by high and steep mountain 
ranges; why others had a rough climate when exposed on .their 
northern side. The teacher was well inft)rraed, and he adapted his 
information to the capacity of his pupils. 

One part of his lesson, outlined in the following summary, was 
especially well received : 

" The Erz-Gebirge (Ore Mountains) were once full of silver mines. At 
the beginning of the sixteenth century, in the time of Martin Luther, 
these mines drew a great number of people to vSaxony, and particularly 
to that range of mountains. When the mines ceased to yield, the 
population, not being so fluctuating as it is now, was obliged to seize 
upon other modes of occupation. The slopes of the mountains, being 
well provided with various kinds of woods, ofi:ered material for a 
variety of woodworking industries. The slopes being steep, the 
mountain brooks were turbulent and gave an opportunity to build 
mills, which were first used for various purposes. Lately, when the 
textile industry grew, this water-power was used to serve that industry. 
The woods soon disappeared from the Erz mountains — they were 
literally used up. So the people had to resort to manufacturing pur- 
suits almost entirely — agriculture being impossible. Today the popu- 
lation of the kingdom of Saxony is the densest in Germany, and, aside 
from that in Belgium, the densest in Europe." 

It was cause and effect constantl}', and the attention and 
responsiveness of the boys were truly deliohtful. 

102. The Art of Questioning-. — In treating^ of the 
Catechetical Method in Pedagogics of History, considerable 



124 PEDAGOGICS OF GEOGRAPHY. § 5 

stress was placed upon its importance as an element of suc- 
cess in teaching. But to a teacher, the value of skill in this 
art is so great that it is deemed best to resume the subject 
in this Paper and present it more fully. A teacher may be 
scholarl}', have an admirable faculty for illustrating what he 
would teach, and be gifted with that wonderful magnetic 
power of securing and holding the attention, but if he is 
weak in the matter of asking connected, relevant, and sug- 
gestive questions, he will be unable to obtain the best 
results. It is a distinctly analytical process, for there must 
lie in the mind of the questioner a sharp logical outline of 
the entire subject. Every part must be properly coordi- 
nated with every other part, and the cjuestioner must be 
able to make every question tell in just the place and order 
required. 

Questioning is called an art on account of its practical use- 
fulness, but it is at the same time a science, for in its best 
development its methods of procedure are regulated by a 
code of principles and laws that are purely scientific. These 
laws and principles have not, so far as the writer knows, 
been reduced to scientific form and order. If they were, 
doubtless they would be found of extreme value to stu- 
dents of many professions such as law, medicine, and teach- 
ing. It is not proposed to attempt here anything like a 
scientific treatment of the subject, but instead, to give such 
suggestions and illustrations as may seem likely to be of use 
to the student of pedagogics. 

103. Classiflcatioii of Questions. — With reference to 
their purpose, questions may be divided into three classes: 

1. Preliminary or Experimental Questions. — By means 
of questions the teacher ascertains the condition of the 
pupil's mind with respect to the subject under considera- 
tion. This is as necessary as diagnosis is in medical prac- 
tice, and in many respects resembles it. The pupil may 
know a subject thoroughly; he may know it partially, but 
not as a connected whole ; or he may know nothing whatever 
about it: which of these conditions of mind is the fact is 



§ 5 PEDAGOGICS OF GEOGRAPHY. l^o 

quickly and certainly ascertained by a few preliminary 
questions, 

2. TJic Didactic, or Iiistrnctioiial Question. — This form 
of question is intended to lead the pupil on step by step from 
what he knows of a subject to what he must know in order 
to fully imderstand the subject. This is in fact a method 
by which a pupil becomes in a manner his own instructor. 
He is compelled to consider carefully every step as he is led 
along by his questioner; and, if he would follow, his inter- 
est and attention must not flag even for a moment. The 
teacher must himself know his subject thoroughly, and he 
must, besides, understand the exact condition of the pupil's 
mind; otherwise, we shall have an instance of the blind 
leading the blind. 

3. The Question for Testing, or Examination. — When a 
subject has been carefully and thoroughly taught, it is, cus- 
tomary in all schools to require that the pupils shall show 
that they arc actually in possession of a satisfactory knowl- 
edge of it. This is done by examination questions covering 
the matter that has been studied. Very frequently it hap- 
pens that relative rank and subsequent honors are deter- 
mined and assigned as a result of these examinations. To 
the pupil, therefore, the examination question is a very seri- 
ous matter, although its instructional value is very slight 
indeed. 

104. Remarks on the Foregoing Classiflcation. 

Of these three varieties of questions, the first is very impor- 
tant indeed. It would be a waste of effort and often perilous 
for a physician to administer medicine without finding out 
the exact condition of his patient; but such a proceeding 
would be exactly paralleled by a teacher that should neglect 
to ascertain the deficiencies and weaknesses of his pupils 
before beginning their instruction. To ascertain this, it is 
obvious that thorough knowledge and a high degree of skill 
in the teacher are necessary. 

But it is especially in the didactic questioning that the 
opportunity occurs for the greatest efficiency in the art of 



12r> PEDAGOGICS OF GEOGRAPHY. § 5 

asking' questions. It is an art, too, that cannot be acquired 
by a study of the rules and principles of dialogue. It is con- 
ditioned on a number of things : 

1. As has already been stated, the questioner must have 
a thorough acquaintance with the matter to be taught. 

2. He must know in just what respect the pupil's knowl- 
edge is defective. 

8. He must be able to keep steadily before his own mind 
the exact matter he wishes to teach. 

4. He must be suiSciently expert in the nse of language 
to formulate questions that will convey to the pupil's mind, 
clearly and without ambiguity, the exact meaning intended. 

0. He must be able to formulate series of questions that 
are the best for his purpose in matter and order. 

In short, the teacher that would be successful in the art 
of didactic questioning, must be a thorough scholar with a 
very clear head, a strong sense of logical order, and an 
admirable command of language. 

The third variety of question — that for examination or 
testing — is a comparatively simple matter. For examina- 
tion questions arc usually written ; and, being miscellaneous, 
they require no logical arrangement, nor is any special 
scholarship needed in their construction. 

105. A Reminiscence. — A good many years ago it was 
among the duties of the writer to be the teacher of the 
gradviation class in the high school of one of our large east- 
ern cities. One of the subjects taught was geometry. It 
happened that before the pupils reached their graduating 
year they passed through the hands of a succession of most 
excellent teachers, and they were, in consequence, admira- 
bly prepared for the severe work of their last school year. 
No task could be more delightful than to teach such pupils. 
They were wonderfully eager to learn, and their mental 
alertness was remarkable. They, however, were not the 
only learners; their teacher also learned many things. He 
learned, for example, the extreme skill required in didactic 
questioning. That it is incomparably better to question 



§ 5 PEDAGOGICvS OF GEOGRAPHY. 127 

than to explain, as teachers do when they say, "Pay atten- 
tion now, and I will explain this matter"; this was another 
of the lessons he learned. And again, he found out that 
there is admirable discipline for the pupil if he himself is 
required, by asking the questions, to lead his fellow that 
"sees but dimly." "You have heard John's recitation," the 
teacher would say; "it shows that he does not quite under- 
stand why A B C is equal to E F G. Who will imdertake to ask 
John the series of questions that will make clear to him the 
missing links in his argument ? " The hands would go up all 
over the room, and some one would be designated to undertake 
the task, with the understanding that the rest of the class 
would criticize the questioner when he was done. The 
excitement and interest were indescribable. Many of these 
questioners became extremely skilful by practice ; and, with- 
out doubt, the training was as valuable as that derived from 
the study of g-eometry itself — perhaps more so. Another 
great advantage that came from delegating this work to the 
pupils was in the fact that the teacher was required to say 
but little; and this, believe me, is always a great gain in 
the recitation room. 

106. Socrates as a Teaclier. — Socrates has, even yet, 
after nearly two thousand four hundred years, the reputation 
of having been the greatest of the world's teachers. He had 
no great school, like the Lyceum of Aristotle or the Academy 
of Plato. He taught more as a mere incident of his every- 
day life than as a business or profession. His pupils paid 
him nothing except in affectionate devotion. Where he 
happened to be he taught; and his pupils, who followed 
him wherever he went, listened to his discussions. His 
charm as a teacher was purely intellectual, not personal, for 
physically he was not an Apollo. On the contrary, he was 
reputed to be the ugliest man in Greece. 

At the time of Socrates, Athens was the intellectual center 
of the world ; and it was, moreover, the home of many men 
of wealth. Attracted by the Athenian love of learning and 
T)y the large fees that were readily paid by rich men for the 



128 PEDAGOGICS OF GEOGRAPHY. § 5 

education of their sons, many men of great reputation for 
skill in teaching' logic, disputation, politics, and other 
matters, came to Athens and set up schools. Socrates 
delighted to seek out these men of reputed wisdom and 
question them about the matters they professed to under- 
stand. The interview was invariably disastrous to the 
sophist that met him in dialectics. He had no code of 
doctrine or opinion to promulgate ; he professed to be only 
an inquirer — a seeker after truth. He insisted that the 
greatest impediment to real knowledge is fancied or unreal 
knowledge, and that the first duty of the teacher is to pre- 
pare the mind for the reception of knowledge and to convince 
the pupil of his lack of it ; to awaken him to a keen desire 
for learning, and to stimulate an earnest search for it. 

Perhaps the best way of showing his method is to translate 
one or two portions of Socratic dialogue from the writings of 
Plato, who was the gTcatest pupil of the old philosopher. 

107. The Method of Socrates. — The first specimen 
of dialogue given here is between Socrates and one of his 
disciples called Meno. This young man was of the kind 
having an exaggerated notion of his own wisdom and 
learning; but he had been probed by his master imtil he 
began to have an imcomfortable sense that he was less wise 
than he had supposed himself to be. Smarting under this, 
he says, 

''Why, Socrates, you remind me of that broad fish called 
the torpedo, which causes a numbness in the person that 
touches it. For, in truth, I seem benumbed both in mind and 
mouth, and know not what to reply to you ; and yet, I have 
often spoken on this subject with great fluency and success. " 

Socrates does not reply directly to Meno, but calls a young 
slave boy, an attendant of Meno, and questions him. Draw- 
ing a square on the ground, he says, 

" My boy, do yoii know what figure this is ? " 

"Oh, yes; it is a square." 

"What do you notice about its lines ? " 

"That all four of them are equal." 



§ 5 PEDAGOGICvS OF GEOGRAPHY. 120 

"Could there be another spaee like this, only larger or 
smaller ? " 

"Certainly." 

"Suppose the side of the square were two feet long" 
instead of one foot; how many square feet would there be 
in the figure ? " 

"Twice two." 

" How many is that ? " 

"Four." 

" Would it be possible to make another square twice as 
large as this ? " 

"Yes." 

" How many square feet would it contain ? " 

" Eight." 

"Then how long will the sides of such a square be ? " 

" It is plain, Socrates, that it will be twice the length, or 
four feet. " 

"You see, Meno, that I teach this boy nothing, I only 
question him. And he thinks that he knows the right 
answer to my c^uestion; but does he know ? " 

" Certainly not. " 

" Let us return to him again." 

" My boy, you say that on a line four feet long a square, 
having a space of eight square feet, may be made; is it so ? " 

"Yes, Socrates, I think so. " 

" Let us try then. Is this the line you mean ? " 

" Certainly." (He completes the square.) 

" How large is the square now ? " 

" Why, it is four times as large." 

" How many square feet does it contain ? " 

" vSixteen." 

" How many ought double the square to contain ? " 

"Eight." 

After some questioning, the boy suggested that the side 
should be three feet long. 

" If, then, it should be three feet long, we should add the 
half of the first line to its own length, should we not ? " 

"Yes." (Socrates draws the square.) 



130 PEDAGOGICvS OF GEOGRAPHY. § 5 

" Now, if our first square contained twice two square feet 
and our second four times four, how many does this contain ? " 

"Three times three, or nine, Socrates." 

" But how many should it contain ? " 

" Only eight, or one less than nine." 

"Well, now, since this is not the line on which to draw our 
square, tell me how long it should be." 

"Indeed, Socrates, I do not know." 

"Now, Meno, observe what has happened to this boy: 
you see that he did not know at first, neither does he now 
know. But he then answered boldly because he fancied that 
he knew ; now he is quite at a loss, and though still as igno- 
rant as before, he does not think he knows." 

"What you say is quite true, Socrate.s. " 

" Is he not now in a better state with respect to the mat- 
ter ? " 

" Most assuredly he is." 

" In causing him to be thus at a loss, and benumbing him 
like a torpedo, have we done him any harm ? " 

" None at all." 

"We have at least made some progress toward having him 
know his true position; for now, finding that he knows 
nothing, he is more likely to inquire and search for himself. " 

This dialogue illustrates one of the best methods of arous- 
ing the curiosity that stimulates self-effort and investigation. 
Before giving a lesson or entering upon a difficult subject, 
it is often a good plan to cause the pupil to realize his 
ignorance and to feel the need of your instruction by asking 
him a series of searching judicious questions. 

108, Anotlier Specimen of Soeratic Dialogue. 

The following is a translation from the " First Alcibiades " 
of Plato. It gives an imaginary conversation between 
Socrates and his favorite pupil Alcibiades. 

Socrates. Hold, now, with whom do you at present con- 
verse ? Is it not "with me ? Alcibiades. Yes. 

Socr. And I also with you ? Ale. Yes. 

Socr. It is vSocrates then that speaks ? Ale. Assuredly. 



§ 5 PEDAGOGICvS OF GEOGRAPHY. 131 

Soc!'. And Alcibiadcs that listens ? ^l/c. Yes. 

Socr. Is it not with language that Socrates speaks ? Ale. 
What now ? of course. 

Socr. To converse and to .use language, are not these then 
the same ? A/c. The very same. 

Socr. But he that uses a thing, and the thing used — are 
these not different ? .lie. What do you mean ? 

Socr. A currier, — does he not use a cutting knife and other 
instruments? Ale. Yes. 

Socr. And the man that uses the cutting- knife, — is he 
different from the instrument he uses ? A/c. Most certainly. 

Socr. In like manner, the lyrist, — is he not different from 
the lyre he plays on ? A/c. Undoubtedly. 

Socr. This, then, was what I asked you just now, — does 
not he that uses a thing seem to you always different from 
the thing used ? A/c. Very different. 

Socr. But the currier, — does he cut with his instruments 
alone, or also with his hands ? A/c. Also with his hands. 

Socr. He then uses his hands ? A/c. Yes. 

Socr. And in his work he i;scs also h!s eyes ? A/c. Yes. 

Socr. We are agreed, however, that he that uses a thing, 
and the thing used, are different ? A/c. We are. 

Socr. The currier and the lyrist are, therefore, different 
from the hands and the eyes with which they work ? A/c. 
vSo it seems. 

Socr. Now, then, does not a man use his whole body ? 
A/c. Unquestionably. 

Socr. But we are agreed that the person using a thing is 
different from the thing used ? A/c. Yes. 

Socr. A man is, therefore, different from his body .'' A/c. 
So I think. 

Socr. What, then, is the man ? A/c. I cannot say. 

Socr. You can at least say that the man is that which uses 
the body? A/c. True. 

Socr. Now, does anything use the body but the mind ? 
A/c. Nothing. 

Socr. The mind is, therefore, the man? A/c. The mind 
alone. 



132 PEDAGOGICS OF GEOGRAPHY, 



BOOKS OF REFEREKCE. 

109. Keed foi* Books of Reference. — No teacher can 
be highly successful in teaching geography, or, indeed, any 
other subject, without having a good supply of the latest and 
best books of reference. Books are the tools with which the 
teacher works, and are just as necessary to him as the appro- 
priate tools are to the carpenter or the machinist. If his 
work happens to be in the neighborhood of a public library, 
he may perhaps borrow all the books he wants, but it is vastly 
better to own them, just as it is better for the industrial 
worker to own the tools he uses. These necessary books 
need not be purchased all at once, but the collection should 
be systematically increased as means and opportunity offer, 
and every purchase should be made with extreme care. Of 
course, no teacher can afford to buy everything that bears 
upon the subjects he teaches, but with a little finesse he can 
establish a small school library that may be gradually enlarged 
at the expense of the school board or by means of money 
received as the result of any of the various legitimate enter- 
prises commonly resorted to for such objects. His success 
will be measured by his ability to invest the otherwise dry 
matter of the textbook with human interest and reality, and 
to do this he must have a wider knowledge of his subject than 
he can possibly get from the book studied by the pupils. 

1 10. Reiiiai'ks on tlie rolloAvin^ Tjist. — In the list that 
follows no attempt is made to include everything of value to 
the teacher of geography; for a complete list would fill a 
large volume. Only a limited number of works known to 
be excellent are given. For more extensive lists the student 
is referred to the catalogues of the various publishers and to 
the special works on bibliography. One of the best of the 
latter publications is Monroe's " Bibliography of Education," 
edited by our Commissioner of Education, Dr. William T. 
Harris, and published by D. Appleton & Company, New 
York Citv. 



§5 



PEDAGOGICS OF GEOGRAPHY. 



133 



Some of the books in the list are mere stories of imaginary 
travel and adventure, but they are all valuable, since in their 
geography and in the manners and customs of the peoples 
described they are all pretty true to the facts. vSuch books 
are of great value in developing the "geographical instinct," 
and they should find a place in every school library. 



111. Books of Travel and Adventure. — 

Children of the Cold. Frederick Schwatka. Casscll &■ Co. 
A story of the Eskimos met by the author in his Arctic travels. 

Seven Llltle Sisters. Jane Andrews. Lcc & Shcpard. 
An admirable preparation for the study of geography. 

Seven Little vSisters Prove their Sisterhood. Andrews. 
Lcc & Shcpard. A sequel to the above. 

Little People of Asia. Olive Thorne Miller. E. P. 

Duttoii &• Co. 

Lost in the Jungle. 1 ^ 

•^ _ j I)u Lhaillu. 

Harper ^r Jh-otJicrs. 



vStories of 'i'HE Gorilla Couni 
Wild Life under the Equator. 
Great African Travelers. Kingston and Low. 
Icdicc &" So//s. 



Roiit- 



Nclson & So/is. 
Hale. Roberts Brothers. 



Heroes of the Desert. 

Stories of Discoverv. 

Stories of Adventure. 

Stories of the Sea. J 

Boy Travelers in Japan and China. 

Boy Travelers in vSiam and Java. 

Boy Travelers in Ceylon and India. 

Boy Travelers in Egypt and the 
Holy Land. 

Boy Travelers through Africa. 

Boy Travelers in the Russian 
Empire. 

Boy Travelers on the Congo. 

Boy Travelers in Australasia. 

Boy Travelers in vSouth America. 

Java, the Pearl of the East. Higginson. 
Mifflin & Co. Full of information. 



Knox. Harper & 

Brothers. 

These books are 
richly illustrated 
and have neces- 
sary maps. The 
series is a very 
valuable one. 



IlouisJiton. 



Knox. 

Harper & 
Brotlicrs. 



134: PEDAGOGICS OF GEOGRAPHY. § 5 

NiMROD IN THE North. vSchwatka. Casscll & Co. Hunt- 
ing and fishing" adventures in the polar regions. 

Wild Men and Wild Beasts. Gumming. Charles Scrib- 
iwr's Sons. 

The Young Nimrods in North America. 

The Young Nimrods Around the World. 

The Voyage OF the Vivian to the North 
Pole. 

Mutineers of the Bounty. Belcher. Harper & Brothers. 

In the Wilderness. Charles Dudley Warner. HoiigJiton, 
Mifflin & Co. 

Round my House. Hamerton. Roberts Brothers. 

Along the Florida Reef, Holder. P. Appletoti & Co. 

Aunt Martha's Corner Cupboard. Kirby. 

Each and All. 

Home Studies in Nature. Treat. Harpers. 

Works of John Burroughs. 

Two Years Before the Mast. Dana. 

Mexico. Blake and Sullivan. Lee & Shepard. 

Captain Bonneville. 

Famous Travels and Travelers. 

The Great Navigators of the 
Eighteenth Century. 

The- Great Explorers of the 
Nineteenth Century. 



Verne. Scribners. 



113, Miscellaneous Books on Travel and Geog- 
raphy. — 

Comparative Geography. ) „. , . r^ i ^ 

^ ^ c Ritter. American hook Co. 

Geographical vStudies. ) 

Earth and Man. Guyot. Scribners. 
The Earth and its Inhabitants. E. Reclus. Apple- 
ton. (U vols.) 

Bird's-Eye View of the World. O. Reclus. Ticknor. 
Brown's Countries of the World. 
Brown's Peoples of the World. 
Physiography. Huxley. Appleton. 
■ The Earth. Reclus. Harpers. 



§ 5 PEDAGOGICS OF GEOGRAPHY. 135 

The Realm of Nature. Mill. 

Volcanoes. A volume among the "International Scien- 
tific Series." Applet o)i. 

Reports of Challenger Expeimtiox. 

Bird's-Eve View of Central and South America. Bates. 

Humboldt's Travels. 

Peru. vSqiiier. 

Sixteen Years in Chili and Peru. vSutclilTe. 

Journey in Brazil. Agassiz. 

Adventures in Trinidad and up the Orinoco. Kingston. 

On the Banks of the Amazon. Livingston. 

Between the Amazon and the Andes. Mulhall. 

Up the i^MAZON AND JHE Madeira Rivers. Mathcws. 

What Darwin vSaw. 

Stories of the Nations. Putuam. 

Sinai and Palestine. Dean vStanley. 

Spain and the Spaniards. ) ^^ . . . 

„ -De Amicio. 

Holland and its People. ) 

France. Roberts. 

Greece. Lewis. 

Siberia in Europe. Seebohm. 

Iceland. Taylor. 

Russia. Morfill. 

The Land of the Midnight Sun. Du Chaillu. 

The Florence Stories. Abbott. 

Scotland and the Scotch. 

The Statesman's Year Book. Keltic. Published 
annually. Contains much valuable information concerning 
all the nations of the world. 

Historical Geography of Europe. Freeman. 

The Middle Kingdom (China). Williams. 

The Land of the White Elephant (Eastern Asia). 
Vincent. 

Japan. Reiss. A very complete description of Japan. 

Through Algeria. Crawford. 

Upper Egypt. Klunzinger. 

The Nile and Tributaries of Abyssinia. Baker. 

Life in the Desert. Du Couret. 



13G PEDAGOGICvS OF GEOGRAPHY. § 5 

African Explorations. Livingstone. 

Through the Dark Continent. Stanley. 

Land Journey through Siberia. 

Travels and Discoveries in Northern and Central 
Africa. Denham. 

Among the Huts in Egypt. 

IsMAiLiA. Baker. 

How I Found Livingstone. Stanley. 

The Albert Nyanza. Baker. 

The Lake Regions of Central Africa. Geddie. 

Thirty Thousand Miles' Travel in Australia. Vincent. 

The Country of Dwarfs. ) ^^^ ^j^^.^^^^ 

My Apingi Kingdom. ) 

The Congo. Stanley. 

Voyage of the Vega. Nordenskjold. 

Arctic Voyages. 

Intellectual Development of Europe. Draper. 

Coral and Coral Islands. Dana. 

The Races of Men and thkir Geographical Distribu- 
tion. Peschel. 

The Vegetable World. Figuier. 

Narrative of Four Voyages to the Antarctic Ocean. 
B. Morell. 

Notes of a Naturalist on the Challenger. H. N. 
Mosely. 

Voyage of the Beagle Around the World. Charles 
Darwin. 

The First Crossing of Greenland. Nansen. 

Three Years of Arctic Service. A. W. Greely. 

Structure and Distribution of Coral Reefs. 

The Glaciers of the Alps. John Tyndall. 

The Naturalist on the Amazon River. H. W. Bates. 

New Zealand: its Physical Geography, Geology, and 
Natural History. Von Hochstetter, translated by E. 
Sauter. 

Personal Narrative of Travels in South America. 
Von Humboldt. 

New Lands within the Arctic Circle. J. Payer. 



PEDAGOGICS OF HISTORY. 



i:nti?oductio:n^. 



GENERAI. REMARKS. 

1. Forms of Wi-itteix Th<)iij>iit. — Extended composi- 
tion has been divided into four kinds: Dcsr)'iptioii, Narra- 
tioii, lixpositioii, Argument. Of course, there are many 
other varieties, but these four are the only forms that are 
usually found in textbooks on history. To understand the 
reason why it is so difficult to find a good working manual 
on the subject of history and what qualities should charac- 
terize such a manual, it will be necessary to consider briefly 
these four kinds of composition, 

^. Description. — Description may be of posons or of 
things. A description of anything should present an orderly 
account of the qualities that belong to the object described. 
If a description be in terms that are commonly used, it is 
ordinary or popular ; if it introduces the technical terms 
employed in some particular science, it is a .yr/tv/Z/^r descrip- 
tion. 

3. Narrative. — Narrative bears the same relation to 
acts and ci'cnts that description does to persons and things. 
A narrative, as well as a description, may be either minute 



2 PEDAGOGICS OF HISTORY. . § 6 

or cursory — it may descend to the smallest particulars, or 
it may give only the most conspicuous and striking facts in 
a series of happenings. 

The items that make up a narrative should follow, first, 
the order of tunc. It will appear, later, that in this require- 
ment consists the principal difficulty in historical writing. 
In the nature of things, events that together make up a com- 
plex whole succeed one another in time, and an account of 
them is more vivid and more easily remembered if, in rela- 
ting them, the orderof their occurrence is observed. Indeed, 
the most striking excellence in a sentence, a paragraph, or 
a sustained account of any matter, is this observance of 
chronological order in the arrangement of its elements. In 
this respect, more perhaps than in any other, consists the 
difference between the work of our best writers and that of 
inferior waiters. 

Secondly, besides the order of time, a narrative should 
observe the order of logical sequence or relative iiiiportaiice. 
In every narrative will be found many passages in which the 
element of time does not enter. Thus, the explanation of 
motives, of the purpose, results, or consequences of acts or 
events, of surrounding or accompanying circumstances — 
these and many other matters are of this nature. An excel- 
lent illustration of what is meant by logical sequence in a 
narrative, is found in the paragraphs introductory to the 
" Chimes," by Charles Dickens. Edgar A. Poe's prose works 
furnish some of the best examples of logical arrangement of 
particulars that can be found in literature. Let the student 
try the experiment of rearranging the sentences or the para- 
graphs of that author, and he will feel the force of what is 
here stated. 

4. Exposition.— Exposition is neither more nor less 
than explanation. Like all explanation, it should be clear ; 
it should contain nothing intended to arou.se emotion, but 
should be addressed to the intellect alone. As is the case 
with narrative and description, it should, in the arrange- 
ment of its matter, observe the order of time, if time is an 



§ 6 PEDAGOGICS OF HISTORY. 3 

clement, and, where the element of time does not enter, of 
logieal sequence. 

A definition is the simplest form of exposition. An expla- 
nation of an example in mathematics, an account of the 
action of a drug-, or an explanation of a chemical reaction 
are examples of exposition. In writing a history of the 
United States, the author would find it necessary to suspend 
his narrative in order to explain our relations with England, 
the mutual feeling between the countries, and many other 
matters neither narrative nor descriptive. 

5. Arg'iiiiieiit. — It is no ])art of the work of a hist(.)rian 
to introduce argument into his writing. He should content 
himself with the presentation of facts and events; and, 
accordingly, it is very unusual to find in history anything in 
the nature of distinctly expressed argument. Occasionally, 
indeed, we find exposition colored more or less by attempts 
to convince the reader of the correctness of some view held 
by the author. Everything of this kind, however, is very 
much out of place in a history. Other tilings being equal, 
the excellence of a work on history increases with its 
impartiality — the absence of any expression of the author's 
opinion — the absence of argument and of matter intended 
to appeal to the emotions of the reader. 

6. Histoi'.v Consists of the First Thi*ee of These 
Forms of Coiin>ositioii. — That history should consist 
almost, if not entirely, of description, )iarrativc, and expo- 
sition in varying proportions will be evident to the stiident. 
Anything else should be in the nature of quotation for pur- 
poses of illustration. It must not be assumed that these 
three varieties of composition are always, or even often, 
found separate. They are combined in all proportions, and 
it is often difficult to determine which predominates in a 
given paragraph, section, or chapter. 

In order to render intelligible the narrative of some event, 
say a battle, a description of the battle field, its surround- 
ings, and the roads leading to it; or an exposition of some 
principle of military science, or of the advantages of some 



4 PEDAGOGICS OF HISTORY. § G 

particular formation of the attacked or the attacking forces; 
or some explanation of how the armies came to meet at that 
particular time and place — any one or all of these may be 
necessary. 

It is clear, therefore, that written history is made up of 
description^ cxpositio)i^ and explanation in varying propor- 
tions, and that in all these, chronological order should be 
followed when time is an element. When considerations of 
time do not dominate the arrangement of historical matter, 
as is generally the case in explanation and exposition, then 
the laws of cause and effect — of logical sequence- — should 
determine the succession of parts. Historical arrangement 
in the nature of climax is peculiarly effective. Gibbon, 
Macaulay, and many others among the writers of history 
have realized in this fact one of the principal charms of his- 
torical composition. 

The writer may be permitted to observe, at this point, 
that interest is added to a lesson in history, and the opera- 
tion of the law of association is aided, by having the pupils 
examine the text for the purpose of determining to which 
class of composition the several paragraphs belong. This is 
not to divert attention from the subject matter considered as 
history, but to illuminate, and add to the interest of, the 
text. 

'7. l^nilineal and Miiltilineal AV^riting. — Professor 
Bain, in speaking of the different kinds of composition, 
emplo3'S the words iinilincal, lulineal, and vinltilineal. These 
words contain the Latin word liiunn, "flax," "thread," and 
very happily characterize the varieties of description, explana- 
tion, exposition, and argument. 

If one were required to describe any simple object, or to 
write a narrative of the doings of any person during an entire 
period, either of these would be an example of unilineal com- 
position. The subject is not complicated by any side issues. 
There are no threads on either side of the main thread of the 
narrative or the description that are necessary to the com- 
pleteness. No special literary art or skill is requisite in this 



§G PEDAG()(;iCS OF HISTORY. 5 

kind of composition — only the ability to tell a •'plain nnvar- 
nished tale." 

History, however, is not uiiiliiical, but multilincal. Numer- 
ous threads must be taken up, carried into, and incorpo- 
rated with, the principal thread; and this must be done in 
such manner as to g'ive unity to the whole, and preserve its 
interest and intelligibility. This, it is easy to see, is a very 
difficult task. The sequence of events with respect to time 
cannot be observed, for, after tracing the main thread of the 
narrative through a certain period, the writer is compelled 
to go back again and again, and follow the minor threads to 
the point where he broke off. An unavoidable consequence 
is that the reader is confused by the multitude of extrinsic 
incidents making up the complete story, the effect upon his 
inind is weakened, and he is quickly wearied. 

The multilineal treatment may be likened to a river with 
its tributaries, or to a tree with its innumerable branches, 
branchlets, and twigs. Every one has noticed the fact that 
a tree with an axial trunk, like the pine or the poplar, is 
much more pleasing to the eye than one with a solvent trunk, 
and that, when a tree is covered with foliage, hiding its 
branches and making it a unit to the eye, its beauty as a part 
of the landscape is much enhanced. It is a general principle, 
indeed, that simplicity and symmetry are two elements 
indispensable to the beautiful. This is in accordance with 
the well known Theory of Pleasure and Pain, that a sense of 
baffled effort on the part of the mind to comprehend is pain- 
ful, and that the reverse is pleasurable. Order, simplicity, 
logical sequence, and symmetry afford us pleasure; while 
complexity, involvement, and discord hinder and perplex 
the action of the mind and create an effect that is more or 
less displeasing or painful. 

The fact that historical works are necessarily vniltilincal 
constitutes the chief obstacle to unity, and explains why the 
world has furnished so few great historians. Some one has 
remarked that a satisfactory history of the Jesuits has never 
been written, and perhaps never can be written, the reason 
being that the Order has been involved and active in the 



(; PEDAGOGICvS OF HISTORY. § G 

politics, and has intiuenccd the history, of every country in 
Europe. A history of this organization would therefore be 
painfully multilineal. 

8. Unsatisfactory Textbooks on History. — From the 
considerations stated above, it is easily seen that to write an 
interesting textbook on history is a difficult matter, and it is, 
in fact, a task that has rarely been accomplished. Many a 
work of fiction, w^hile vividly conceived and ably written, has 
failed on account of the introduction of too many characters. 
When Henry Ward Beecher was writing his novel "Nor- 
wood " as a serial for the New York Ledger, some one asked 
him how he meant to dispose of the many people that he had 
brought into the work. He is said to have replied that he 
would have them killed in a railroad accident. The novel 
was wonderfully well written, but no one hears of it now, 
and this is chiefly owing to its highly multilineal character. 
How different is the case with the story of Robinson Crusoe. 
Perhaps no .single fact has contributed so much to make 
Defoe's story an immortal classic as its wiilincality. The 
attention is constantly centered on the hero, and even when 
Friday appears on the scene, there is still but one thread in 
the narrative. The newcomer falls into the same relation in 
the narrative as the goats and the parrot sustain to Crusoe. 
Everything is subordinated to the movements, the hopes, the 
fears, and the plans of Crusoe. Bunyan's " Pilgrim's Prog- 
ress " loses much of its interest when the attention of the 
reader has to be divided between Christian and his wife. 
The story ceases to be unilineal and becomes biliiieal. The 
rare art of weaving into a single fabric, elements that seem 
unrelated and incongruous, must characterize the writer of 
a good textbook on history. 

As a consequence of the difficulties mentioned above, our 
textbooks on history lack unity and interest, and afford but 
little help to the pupil or the teacher. It follows, of course, 
that— 

9. Children Dislike the Study of History.— It is a 

fact well known among educators that students of history 



§ 6 PEDAGOGICS OF HISTORY. 7 

rarely like the subject. They often delight in the study of 
grammar, of geography, of mathematics, of language, or of 
science, but, generally, their feeling about the subject of 
history is, "I hate it." Occasionally, but not often, a class 
is found of which the contrary is true. This suggests the 
question of zvJiy. Is there indeed something in the subject 
itself that should cause it to be, both to teacher and pupil, a 
source of weariness and disgust ? We think not. Certainly 
interest and pleasure ought to be found in the story of 
what men and nations have done and suffered, of how 
the slow march of progress has been accomplished, and of 
what the world's great activities have been. Without hesi- 
tation, one might assume that ncj subject of study could 
be of greater human interest, or furnish a more effect- 
ive stimulus to hopes of high endeavor. Rut, as taught 
in our schools, history fails, with some rare exceptions, 
either to inspire the ambition of its students, or even to 
interest them. 

10. A General Principle in Teacliinsf. — As has been 
remarked, we occasionally find a teacher able to arouse in a 
class the greatest interest and enthusiasm in the study of 
history. Another teacher, after greater effort, finds the sub- 
ject wearisome to himself and hateful to his pupils. The 
same thing happens with other subjects. The writer has 
seen entire classes of students extraordinarily interested in 
geometry — so much so, indeed, that they were disposed to 
neglect every other study — and he has known the opposite 
condition of things. Such facts have led educators to the 
recognition of the principle — 

Any subject that is 7.'r// taught is interesting to the student. 

It follows, therefore, that when pupils dislike an}' given 
study, the teacher is responsible. It is not much in extenua- 
tion to urge that textbooks are faulty, for teachers of real 
ability rely little upon them. Tliey themselves are the text- 
books — living textbooks, instinct with enthusiasm and inter- 
est — a hundredfold more instructive than books supplied by 



8 PEDAGOGICvS OF HISTORY. § (j 

the publishers. In fact, our best teachers are, in many sub- 
jects, more hindered than helped by textbooks. It is the 
contact of mind with mind that is in the best sense effective 
— not the contact of mind with "cold type." 

11. Histoi*y Difflciilt to Teaeli Well. — It is not easy 
to achieve success in teaching any subject, and this is espe- 
cially true of the history of the United vStates. Apart from 
want of skill and experience in the teacher, there are several 
other causes that contribute to failure. The principal of 
these are the want of unity in the subject itself, arising from 
its multilineal character, and the faultiness in textbooks. As 
has already been stated, for many hundreds of years it has 
been thought by writers of history that "the king is every- 
thing and the people are of no account." Hence, during all 
this time, history has been a record only of battles and the 
movements of armies, the intrigues of courts, and the rise 
and fall of kings. The social and political, the commercial 
and industrial history of the nations ruled by these kings, 
the interplay of forces affecting the general weal, and the 
progress and effect of science and invention, are regarded as 
of no importance. Our histories have told us nothing of the 
national life at large — its busy activities, its changing opin- 
ions, with their causes and results; nothing of the nation's 
industrial and commercial developments, and the means by 
which they were eff'ected ; nothing of tlie ethical forces 
operating to create national epochs; only the story of its 
generals, and the wars in which the}^ figured, of the 
triumphs and failures of its politicians and its rulers that 
come and go. 

The matters relating to the daily life and activities of a 
nation make up the soul of history, so to speak; but what 
we reall}^ find in our textbooks is only the body — the mere 
skeleton of history. The true logic — the correct interpreta- 
tion — of human happenings is discoverable only from these 
omitted matters. And, hence, the teacher's opportunity to 
interest and to instruct truly and rightly is lost, unless he has 
informed himself by seeking for the whole truth where alone 



§ PEDAGOGICS OF HISTORY. 9 

it may be found — in the records of the growth and progress 
of the nation itself. 

13. The Purpose in the Study of History. — In the 

"study of any subject, there is, or should be, some definite 
advantage in view. Some gain in discipline of mind or of 
body, or some practical usefulness, or both, should be clearly 
proposed as the result of the study; otherwise history should 
be neglected. In general terms, every subject that we study 
should aid us in living more completely — physically, mentally, 
morally, socially, esthetically. When rightly taught, apart 
from its value for purposes of mental discipline, history 
primarily enables a man better to understand his duties as a 
citizen. It instructs him in the causes that have led to the 
progress and the decadence of nations, and in the best means 
of assuring the one and of avoiding the other. Not in this 
respect alone is history of value. It contributes to man's 
efficiency in every walk of life by extending his horizon, 
confirming his mental grasp, and liberalizing his opinions. 
To know the consequences of individual and national action, 
to be able with greater certainty to infer the laws that govern 
success and failure among men and nations, to gain the 
inspiration and stimulus that come from knowing the story 
of human achievement and progress — these and many more 
are the ends we should have in the stud)^ of history. The 
highest patriotism requires that this subject should be 
retained in the courses of study of all our schools, public 
and private. 

More especially is it important for a student to have a 
thorough knowledge of the history of his own country — 
nothing so develops and strengthens his sentiment of patri- 
otism, and makes him willing to fight, and if need be, die, for 
national liberty and integrity; nothing aids so much to make 
him not merely a good citizen, ready to obey the laws and 
to discharge in fullest measure his obligations to the State, 
but • also to make him understand the nature of those laws, 
and of his political duties and obligations. 

Surely, then, it is a most important subject, and is worthy 



10 PEDAGOGICvS OF HLSTORY. § 6 

of the teacher's highest ambition to guide his pupils wisely 
and skilfully in its acquirement. 

13. The Teaclier Must KnoAV His Subject Tlior- 
ouglily. — As has been stated elsewhere, if a teacher is to be 
successful in teaching any subject, he must not only be skil- 
ful and resourceful in his profession, but he must be perfectly 
familiar with that subject, both in itself and also in its rela- 
tions and applications. He should know it so well that no 
textbook need be in his hand during a recitation. It is not 
meant by this that he should have committed the lesson to 
memory so as to know exactly when and to what extent a 
pupil reciting has departed from the language of the book. 
The teacher that does this will inevitably bring his class to 
hate the subject, whether it be history or some other study. 
The teacher should have in his mind an outline of the topics 
of the textbook, if one is used by the pupils, and he should 
be able, besides, to lead the pupil to incorporate the lesson 
with the whole of which it is, or should be, a part. In other 
words, history should be taught in such a manner as will 
exemplify not only logical, but also chronological sequence. 
Each event is at first an effect or a result of some cause, and 
later becomes itself a cause. There should be no broken 
links in the chain of events that make up history — no broken 
threads shoiild interrupt the operation of the law of associa- 
tion. Without this law, history becomes only a series of 
unrelated, isolated incidents. 

For a teacher to gain this broader view — this knowledge of 
the philosophy and the logic of history — time, extensive read- 
ing, reflection, and a keen sense of logical connection are 
required. He must be willing to devote his best powers to 
the subject. 

But no one can teach with success the history of any 
country if he knows that alone. He miist know the history 
of other countries. A perfect knowledge of the English 
language implies a large measure of familiarity with all 
langiiages, for they are all more or less related to it and to 
one another. In like manner, the history of each nation of 



g PEDAGOGICvS OF HLSTORY. 11 

the world has been more or less influenced and modified by 
each other nation. The history of the Roman Empire, for 
example, cannot be adequately told unless there is related, 
at the same time, a portion, at least, of the story of all the 
peoples that came under her domination, and by whom her 
history was modified. It follows, therefore, that the teacher 
of history, if he wishes to be successful, must read histoiy 
extensively. The more comprehensive his reading- the wider 
will his views become, and the more will they gain in unity. 
This leads naturally to the question of the teacher's histor- 
ical reading. 

14, .How a Teaelier Should Regulate His Reading;. 

There is not more than one reader in a score that wisely 
utilizes his time. This arises from several causes. Chief 
among these is the fact that only a very small percentage of 
the works on any subject are really valuable or entirely 
reliable. Many of the works on history are in large measure 
fiction, or they are mere garbled compilations of the writings 
of some other author. The teacher, therefore, that would 
make the greatest possible progress in informing himself on 
any subject, should seek the advice of some competent 
authority as to the books to be read, and the order in which 
they should be taken up. In the case of history, this order 
should begin with one or more reliable general compendiums 
that shall enable him to fix in his mind the principal land- 
marks of the subject and their relations as parts of a whole. 
When this has been well done, he is prepared to fill in, more 
or less completely, the details. To do this, he must " read 
ill a straight line.'" The reason for this is apparent. If the 
several steps in an argument, say an algebraic or a geomet- 
rical demonstration, be disarranged, the force and unity of 
the whole are destroyed. So, in reading history. The maxi- 
mum result for the reader is produced only when his order 
of reading accords with the sequence in logical relation, or 
in time, of the events narrated. 

As his reading proceeds, he should make written analyses 
of each book separately, and, later, he should unite these 



12 PEDAGOGICS OF HISTORY. § 

into a single coherent outline. These synopses should be 
placed where he may see them often and become familiar 
with them. The writer remembers calling, many years ago, 
upon a friend engaged in the study of law. At that partic- 
ular time Blackstone was the author with whose works the 
student was engaged. The w^alls of the room were nearly 
covered with papers pinned together and showing an orderly 
outline of the contents of the book as far as it had been 
studied. That friend has since made himself noted for the 
exactness of his legal learning. In a similar manner the 
student of any subject should take precautions against 
anything escaping him that is worth preserving. Such 
ovitlines are perhaps more useful if preserved in a note 
book. Other note books, properly labeled, should contain 
quotations that for any reason are deemed to be of special 
value. 

15. Prose Quotations and Poetry. — The teacher 
should provide himself also with a collection of poems illus- 
trating noted historical events, and with celebrated descrip- 
tions of places, battles, or other matters, for nothing else is 
so effective in causing the past and the distant to seem like 
the vivid present. Macaulay's "Lays of Ancient Rome" ; 
Victor Hugo's description of the Battle of Waterloo; 
excerpts from Carlyle's "French Revolution" or from 
Dickens' "Tale of Two Cities" illustrating the horrors of 
the most dreadful period in French history; Lincoln's 
Address at Gettysburg; "The Isles of Greece," and many 
other passages from Byron relating to Greek and Roman 
history — these and similar quotations can be used with much 
effect by the teacher of history. The object of all such 
auxiliaries is to produce vivid impressions; and upon such 
impressions and upon repetition of effects depends the reten- 
tiveness of memory. With fine natural aptitudes, such a 
course of self-training in his art will, in a few years, place 
the teacher in the rank of experts, and cause him to be 
sought after as one of those whom the world delights to 
honor. 



§ 6 PEDAGOGICS OF HISTORY. 13 

10. Time Given iu Our Seliools to the Study of 
History. — Another obstacle in the way of the teacher of his- 
tory is the shortness of time given to it in our courses of 
study. In many of our schools no attention whatever is 
accorded to the study of general history, and one term, or, 
at the most, two terms, devoted to the history of the United 
States, are deemed sufficient. One consequence of this is 
that textbooks are modeled to suit this slight treatment. 
Some years ago a series of books was prepared, entitled : 
"Fourteen Weeks in Chemistry," "Fourteen Weeks in 
Physics," "Fourteen Weeks in United States History," etc. 
The sale of these books was enormous. Parents, school 
officers, and even teachers fondly imagined that by using 
them great strides could be made in accpiring an education. 
The educated teacher, however, knows that, if a study is 
begun and ended in so brief a period, it can have no value 
worth mention. If a subject is to furnish a mental discipline 
that will change the student from what he was to something 
stronger and better, it must exert its influence for a longer 
period than fourteen weeks. The same may be said of the 
studies that we pursue for the sake of their practical use- 
fulness. 

The " vStory of Schcherezade " consumed 1,001 nights, 
and surely the story of the human race should, in the 
telling, require more than a brief period twice or three 
times a week during 70 school days. Textbooks written 
for the purpose of being completed in such a short time 
can be nothing better than lifeless and fleshless skeletons, 
and the "I hate history" of those that study them is 
inevitable. If history is to have any place at all in our 
schools, let it be a place worthy of the importance and use- 
fulness of the subject. 

Almost all the colleges in this country ignore the subject. 
It is true that some of these higher institutions are beginning 
to recognize that history well taught and thoroughly mas- 
tered is an indispensable element in the education, not alone 
of the man of liberal culture, but also of the enlightened 
citizen and the man of affairs. 



U PEDAGOGICS OF HISTORY. 

PHEPAT? VTIOX FOR TEACHIKG 
HISTORY. 



IT^TRODUCTION. 

ll'. Method Necessary in Study and Teacliiii^. — - 

No work is ever well done that is not carefully planned. 
The engineer that intends to build a ship, a great bridge, 
or a fort determines the excellence of the ultimate result 
by the character of his plans. An orator may possibly be 
eloquent without preparing his address beforehand, but if 
his thoughts and argument, are carefully considered and 
arranged before deliver}-, their effect upon his audiences, 
and their influence upon being read afterwards, will be much 
greater. Similarly, a teacher whose aim is to do his work in 
the most thorough manner possible, must make special prep- 
aration for each lesson. In other words, he must be a stu- 
dent as long as he is a teacher. Every lesson should be 
as carefully planned as a sermon, a poem, or a magazine 
article. There is scarcely a subject that is not capable of 
scientific arrangement. The same is true of the parts — the 
lessons — into which the matter in a textbook is separated for 
the purpose of study and recitation. In the case of history 
this is true in a marked degree. There is a logic of events, 
a philosophy of causation and sequence in the occurrences 
that make up the life of an individual or the history of a 
people. The rules that should regulate the telling of each, 
in whole or in part, are the same. The best teacher of his- 
tory is the one that most accurately discovers and interprets 
the purpose, the causes, and the consequences of historical 
action. This, too, must be done not merely by himself; he 
must lead his pupils to reflection and inferences similar to 
his own. By being himself a student and an investigator, 
he must imbue his students with the same spirit of research. 

18. The Teacher Must Create Anionjif His Pnpils 
a Taste for Historical and Bioj^rapliical Keadinj?. — 



§ G PEDAGOGICvS OF HLSTORY. 15 

Perhaps no teacher has ever succeeded in arousini^ in a class 
of pupils a genuine liking and enthusiasm for history by con- 
fining their attention to a single textbook on the subject. A 
work, to be suitable for classroom use, must be meager in 
details. This is necessarily so on account of the vastness of 
the subject. Such a textbook can, in the nature of the case, 
be only the merest skeleton account of events. In itself, 
therefore, it is certain to be dry and tiresome. If, however, 
the student's reading is so directed as to amplify and give 
life and reality to its briefly stated contents, it matters little 
how concisely they are given. The items in the book become 
mere counters, each significant of a large and interesting 
area that the student has explored. Just as the name of a 
city, a river, a mountain, is but a name, a mere combination 
of letters to one that has never seen them for himself, but 
becomes rich in significance and fertile in suggestion to him 
that has seen them, so is it with these mere catchwords of 
history. 

How greatly is interest in the history of Germany or 
France enhanced by reading historical tales such as were 
written by the woman whose pen-name was Luise Mlihlbach. 
Dumas' novels have contributed more, perhaps, than any- 
thing else to make French history intelligible and a source 
of pleasure. Carlyle's wonderful "French Revolution," 
Dickens' "Tale of Two Cities," and similar works should 
be read before any of the histories of France are attempted. 
An admirable preparation for the history of the United 
States is found in the historical novels of Sims and the 
biographies written by James Parton, detailing the lives 
of noted Americans. 

A teacher, therefore, must ascertain just what there is in 
historical, poetical, biographical, and fictional literature that 
will increase the vividness of effect produced upon the minds 
of his pupils at any given time in their progress. If he does 
this part of his work well, he will give an impetus to their 
love of historical reading that will last throughout life. 

This part of the duty of a teacher of history is of com- 
paratively easy accomplishment, if his work is done in a city 



10 PEDAGOGICS OF HISTORY. § 

or in a large town; but if he teaches in a country district or 
in a small village, he is confronted by a serious obstacle. 
This is owing to the usual absence, from such places, of 
libraries large enough to meet the requirements of successful 
history teaching. 

19. Concerning the Supplying of Books of Refer- 
ence in Country Districts. — To arrange a scheme for dis- 
tributing- books for general reading in small villages and in 
country districts, and for having them properly cared for and 
preserved from loss, is a difhcult problem. About 35 years 
ago an attempt to do this was made in the state of Ohio. 
Whether or not the plan is still in operation there the writer 
does not know. The books, strongly bound in sheep, were 
furnished by the state, and upon their covers was stamped 
the statement that they were public property. The custody 
of a sufficient number to supply a given neighborhood was 
made the duty of the secretary or the chairman of each local 
school board. It devolved upon him to keep the records 
necessary to their proper care and prevention from loss. 
After a time, when his supply of books had been read by all 
the people in the district desiring to read them, he would 
exchange his stock for that in an adjoining district. Owing 
to the carelessness of some of these custodians of the books, 
many were lost or quickly destroyed. Only a state having 
a large fund for educational piu'poses can keep tip such a 
method of supplying reading matter for the general public. 

In the densely populated countries of Western Europe, 
large public libraries are numerous and of easy access. It is 
no wonder, therefore, that the Germans have been able to 
surpass us in the quality of their historical teaching. They 
are the creators of the " Laboratory Method," which some 
educators have tried, with no marked success thus far, to 
introduce into the schools of the United States. There can 
be no doubt that the great success with which history is 
taught in Germany with this method is largely owing to the 
density of population and the consequent easy access to 
books for research and sfeneral reading. 



§ G PEDA(K)GICS OF HISTORY. 17 

The man that can devise a g'ood plan for furnishing exten- 
sive and varied reading matter, not only for the children in 
country schools, but also for the general rural population, 
will be doing much for the progress of our country. This is a 
matter worthy of the most thoughtful attention of the states- 
man and the educator, and it will become easier of accom- 
plishment as our country is developed and the density of 
population increases. 

20. IIo^v Ilistoi'.v Liossoiis Are Usually liCarned. — We 

have all seen the pupils of mediocre teachers prepare history 
lessons, and to any one knowing how it should be done, the 
operation has a pathos in it. The pupil, with his book open 
at the proper place, reads aloud or in a busy whisper, a sen- 
tence or a paragraph, over and over, again and again. This 
reading is always accompanied by a busy movement of the 
lips, an introspective rolling of the eyes, nodding of the head 
to emphasize important words, and by other bodily move- 
ments. Many of the words are not understood, but that is 
a matter of slight consequence to the student, and it never 
occurs to him that the aid of a dictionary would be valuable. 
In the highest probability, he does not own one, and very 
probably the school he attends has no such article among its 
propsrty. The principal thing, as he tmderstands it, is to 
fix the exact words of the author in his memory — the author's 
thoiii^lit and his arrangement of topics are matters of second- 
ary consideration. If he can get the language into his 
memory verbatim ct literatim so as to reproduce it before 
his teacher without varying from tl:e text, he has "no other 
thought beside.' 

Now, if words express no thought, every one knows how 
difficult it is to remember them in a fixed order. 

It is related of a certain actor having a remarkable mem- 
ory, that he was boasting on one occasion of his ability to 
learn quickly and remember anything he chose. A friend 
suggested that perhaps he could compose something the 
actor would find difficult, and sul)mitted a series of words 
having no relation in meaning. Of course, the actor, after 



18 PEDAGOGICS OF HISTORY. § (j 

long study, was compelled to admit his inability to memorize 
the composition. 

Our children that study history in which occur words or 
thoughts they do not understand, are handicapped in much 
the same way. And if, by sheer force of perseverance, they 
do succeed in memorizing such matter, it is forgotten just as 
soon as the recitation, for which alone it was learned, is past. 
Such lessons do not strengthen the memory; they prostitute 
and ruin it. The habit of forgetting is learned much more 
easily than is that of remembering. Moreover, history or any 
other subject, learned in this way, has absolutely no value 
for either practical or disciplinary use. It is by methods 
such as these, that our schools produce so many ca.ses of 
"arrested development." 

21. How History Is Usually Recited. — There are two 
principal methods of "conducting recitations" that arc thor- 
oughly and unmitigatedly bad. Each of these has its slight 
modifications. These methods are : 

1 . T/ic Verbatim Recitation. — Let us suppose that the class 
is ready to recite. The work begins by the teacher asking, 
"Who can tell me where the lesson today begins and where 
it ends?" He opens the manual at the place indicated by 
the pupils, most of whom are not able to answer his question. 
This preliminary question indicates clearly that the teacher 
himself is not prepared for the recitation. If he were not 
provided with a textbook, he would be utterly unable to 
"hear the recitation." The pupils, too, must have their 
books under their desks in order to get the cue when they 
are about to be called to recite. 

"John, you may begin with Lincoln's Administration," 
says the teacher. John recites. "Very good, John, except 
that you said institntion for inauguration, and you left out 
through Baltimore." While John recited, the teacher fol- 
lowed the text with his index finger. John is pleased and 
shows it, for the teacher said, ' ' Very good ! " That miscalled 
word and the omitted phrase did not count either with John, 
the class, or the teacher. " Next; tell us about ." And 



§ 6 PEDAGOGICS OF HISTORY. 19 

so the pitiful exhibition goes on. John, of cour.se, doesn't 
know the inferences that may be made from this farce ; nor 
does his teacher, for if he did, some better way would be 
found. John and his parents think them.selves fortunate in 
havint^ a teaclier so exacting, one that compels the "scholars" 
to study their lessons. The teacher takes occasion to con- 
gratulate the parents on having so studious a son — and he 
really means it. 

2. The Quest ion-and-Aiisivcr Recitation. — For this species 
of recitiition, less preparation on the part of the pupil is 
required than is neces.sary with the method described above. 
He must learn the dates and the meaning of the text .suf- 
ficiently to be able to identify the teacher's questions with 
the several portions of the text. If the teacher is more than 
usually obliging — or stupid — he will a.sk what the lawyers 
call "leading" questions. In such case, the pupil does not 
need to learn even the dates. He will be able to "guess" 
the answer with sufficient accuracy. 

Perhaps the textbook is one of those of peculiar peda- 
gogical excellence that has questions at the bottom of the 
page. By experience, the pupil knows that he will be asked 
those questions and no others, and only those are gone over. 
Not one little wavelet of original thought, or wonder, or 
curiosity, in the teacher or in his pupils, is started by these 
questions. 

In all the foregoing, there is no exaggeration. The writer 
has before him several late textbooks with lists of questions 
on each chapter. Many of them require "yes" or "no" for 
an answer, or they inquire for proper names. It may be 
asked why intelligent authors will write, and modern pub- 
lishers — sensible and hard-headed — will print, such books. 
The answer is that books are made to sell — to meet a "long- 
felt need." As long as county superintendents, and even 
those of cities, will go into schools and ask pupils to "give 
the rule for long division," or will pick up a history and read 
off such questions as are found printed there, and imagine 
they are examining or testing the teacher's work by the pupils' 
ability to answer, so long will books of this kind be found in 



20 PEDAGOGICvS OF HISTORY. g G 

our schools. But the time, let us hope, is not far away when 
this will be changed. 

The method of question and answer will be more fully 
treated under a later topic. 

22. Preparing Lessons From a Textbook. — Consider- 
able has already been said, not only of the teacher's general 
ecjuipment for teaching history, but also of his preparation 
for particular lessons. It is the purpose under this topic to 
treat of the wa}^ in which pupils should be trained to prepare 
lessons from a textbook. 

When a lesson is assigned for study it should be read over 
in the presence of the teacher very much as is done in the 
case of an ordinary reading lesson. The purposes are mainly 
two in this exercise — to clear away verbal difficulties, and to 
bring out the exact m.eaning. 

Now every subject has, or should have, a logical arrange- 
ment of parts. Every paragraph should have some leading 
idea or proposition. In each case, this idea or proposition 
may generally be denoted by a single word or phrase. A 
constant inquiry should be made as to the principal subject 
treated in each paragraph, and the best and briefest expres- 
sion for it. As these are developed one by one, they may be 
written upon the blackboard, and after their relative impor- 
tance as topics, si\btopics, etc. has been determined, they 
should be copied by the pupils. These outlines serve the 
double purpose of emphasizing the meaning and of aiding 
the pupil in memorizing the lesson in the order of topics. 
The lesson should not be regarded as properly learned until 
this skeleton or outline, each item in its proper place and 
relation, as well as the matter to fill up the outline, is firmly 
fixed in the memory. On the other hand, the teacher is not 
ready to meet his class for recitation, until he is perfectly 
familiar with the plan of the lesson and the treatment of 
each subdivision of it: Then both teacher and pupils may 
discard the textbook and each is free to take part, not only 
in recitation, but in a rational and an orderly discussion of it. 
If, in addition, the teacher is fortified by abundant general 



§6 PEDAGOGICS OF HISTORY. 21 

information covering the lesson, and is, besides, master of 
the logical considerations involved, the recitation, when it 
comes, may be made a rare treat to everybody concerned. 

In case the class in question has access to books relating 
to the matters treated in the lesson, the teacher should assign 
to oiie or more of its members the task of preparing to tell 
the rest of the pupils more particularly about some person 
or event mentioned. Of course, the teacher should be able 
to direct the pupils to the books needed for reference. Sup- 
pose, for example, the lesson were about the treason of 
Benedict Arnold and the execution of John Andre. One 
pupil may be asked to prepare himself to give orally or in 
writing a sketch of the life of Arnold, and another that of 
Andre. The former pupil should be referred to Sparks' 
"Life of Benedict Arnold" in his "Library of Anierican 
Biography," Vol. Ill, and the latter to Sargent's "Life and 
Career of Major John Andre," or to the "Atlantic Monthly" 
for December, 18G0. 

These pupils, if they do their work well, which, under 
proper management, is likely to be the case, will theniselves 
be much profited, and will add greatly to the interest of the 
class in the lesson. Certain is it that, to the members of 
that class, the names of Arnold and Andre will thereafter be 
not mere names, but almost living and breathing personages. 
By this means, too, the memory is aided by the enlistment 
of the emotions. Pity for the fate of Andre, and respect for 
him, and horror and loathing for the treason of Arnold, will 
render it simply impossible for the class ever to forget that 
lesson. The writer may be permitted to add that no better 
subject for subsequent composition work can be devised 
than these matters of special investigation. To use them for 
this purpose .serves not only the object primarily intended, 
but also as a review of the history lesson. If a history lesson 
involves any question of geography, and nearly all do, the 
pupils should know that every one is expected to be in readi- 
ness to point out on a map the places where the events hap- 
pened. Still better is it to require that a map shall be 
rapidly sketched tipon a blackboard, and the places indicated 



22 PEDAGOGICvS OF HISTORY. §6 

with respect to other well known and important features. 
This map-drawing nuist not be elaborate or consume much 
time. It need not be accurate; a reasonable degree of 
approximation is all that is required. Anything more con- 
verts the history exercise into a geography lesson. One or 
two minutes should suffice in which to do all the map-draw- 
ing required. It should be added that, as a rule, a mere 
local map, as of a battle, a settlement, or a fort, is not enough 
for the purpose. The boundary lines of the state or country 
in which the locality is included, should be rapidly sketched. 
If two or more states are concerned, as is the case when 
armies are marching from one point to another, the boimd- 
aries should be indicated, and the line of march should be 
shown. 

23. Relics and Mementos. — Another important aid in 
the study of history, and one that has been much insisted 
upon, is that of historical relics and mementos. It is sur- 
prising how many such objects are distributed in any given 
neighborhood — an old flag of the Civil War, or even of the 
Revolution, weapons of antique pattern that were used 
against the Indians or in our wars with Great Britain, arrow- 
heads, Indian pottery, historic letters, ancient documents, 
household heirlooms, and many other objects that have come 
down to us from those distant times. In almost every case, 
the owners of these things are glad to put them at the tem- 
porary disposal of the teacher. The following quotation 
from Mary Sheldon Barnes will illustrate the intense interest 
that children take in these historical relics: 

" In response to a request for flags for a special occasion, a little boy 
of eight years brought me a flag that his father had carried through the 
Civil War. He recounted the battles in chronological order, told me a 
little of the geography, and related an incident that I knew to be true. 
He seemed much interested in the flag, and very proud of the fact that 
his father had held it when one of the bullet holes w^as made in it. The 
class of forty boys and girls, seven to nine years old, asked questions 
eagerly about the flag. ' Where did it come from ? ' ' What makes it 
so dirty ? ' ' What made the holes in it ? ' ' Were they real bullets out 
of a gun ? ' ' What did they want to shoot at the flag for ? ' 'Do you 



§ G PEDAGOGICS OF HISTORY. 23 

think it was right to have a war ? ' One boy said afterwards, ' Couldn't 
it tell a lot of stories, though ! ' The children seemed to feel still more 
interest after I had given them a brief account of it, and several lin- 
gered to see it more closely, and one wished to touch the old flag." 

The historic sense with respect to time is perhaps more 
strono-ly and definitely developed by a study of such relics 
than by any other means. Every teacher of history should 
have in his school as large a collection as possible, and 
should, as thoroughly as possible, understand and know how 
to use it. The great miiseums of the world expend enor- 
mous sums annually in making additions to collections illus- 
trating every department of art and science, and these must 
be studied by scientific writers, if they would make true to 
life the state of things they depict. Nothing is more certain 
than that history can neither be adequately learned nor 
taught without some assistance other than textbooks. The 
teacher, therefore, that means to win a place in the first rank 
of his profession must be willing to give the time and 
thought, and if need be, incur the expense, necessary to 
supply himself and liis pupils with every available appli- 
ance. 

34. Historical Use of Poems and Ballads. — All 

authorities are agreed that of the various aids in teaching 
history none is more valitable than can be obtained from the 
use of poems and ballads. "History describes, poetry 
paints," said W. C. Collar, Head Master of Roxbury Latin 
School. Continuing, he remarks, "There is nothing like 
the magic charm, whether of sublimity or pathos, that poetry 
lends to historical events, persons, and places. ***** At 
the distance of forty years I recall the emotion, tlie tears, 
with which I read in our coimtry school reading book a poem 
that I have never seen since, entitled 'Jugurtha in Prison,' 
beginning 

'Well, is the rack prepared, the pincers heated ?' 

" I knew nothing of Jugurtha, neither when he lived nor 
in what part of the world, nor what he had d(nie that he was 



24: PEDAGOGICS OF HLSTORY. § 

to be starved to death in prison. * * * * * * With what a 
swell of patriotie pride, too, did I as a boy recite, 

' Departed spirits of the mighty dead, 
Ye that at Marathon and Leuctra bled.' 

"Marathon and Leuctra signified nothing to me. I had 
not the remotest idea who were the mighty dead that had 
fallen there, but I felt as if it would have been a joy to have 
shed my blood wath them." 

If the development and cultivation of patriotism is one of 
the important objects of the study of history, and that it is 
there can be no question, the teacher has in the patriotic 
poems, ballads, and songs of his country a potent agency for 
this purpose. " Patil Revere's Ride," and many others of 
Longfellow's poems, Drake's "American Flag," "The Star- 
Spangled Banner," " vSheridan's Ride, " " Barbara Frietchie, " 
" The Bltte and the Gray." vScott's " Breathes There a Man 
With Soul So Dead," and innumerable others are available. 
No emotion of which children are capable is deeper, no senti- 
ment piu'er and finer, than those awakened by a poem 
describing and idealizing heroic achievement or daring deeds. 

This subject has already been adverted to, and is resttmed 
here only on account of its great importance to the teacher 
of history. 

35. Kevie^vs. — Edgar A. Poe in his "Philosophy of 
Composition " alludes to the value of the refrain as an ele- 
ment of beauty and force in poetry. The word is derived 
from the French verb rcfraindrc^ "to repeat. " It is this repe- 
tition, reiteration, review, that is a primary condition of suc- 
cess in teaching any subject. No lesson ought ever to be 
assigned that does not include a review of the preceding- 
lesson, and as soon as any considerable part of a textbook 
has been gone over, in review, a "back review" should be 
begun at the first of the book. And for a fourth time the 
manual should be covered by a rapid general review. 

This is in accordance with Mr. Bain's contention that 
the early work in school should be of limited extent but 



§ (i PEDAGOGICvS OF HISTORY. 25 

thoroughly mastered. He insi.sts that little worth speaking 
of ean be done until the mind has material to work upon. 
Comparisons cannot be made until there are things to be 
compared, classifications are impossible until there are in the 
mind matters that belong in classes, and inferences implied 
by conditions from which they may be deduced. 

Many reviews are doubtless more or less wearisome to the 
teacher and monotonous to the pupils, but much of this may 
be avoided, and interest and pleasure secured, by new and 
more comprehensive generalizations and classifications. A 
teacher's skill may be very accurately gauged by the measure 
of persistence he can induce in a class in struggling long and 
patiently with a diflficulty that is to be mastered. 

At any rate, whether the teacher can make reviews inter- 
esting or not, the early history work, in order to be valuable, 
must be thorough. Without thoroughness, there is no proper 
and certain basis on which to erect later an enduring super- 
structure. Moreover, the habit of patient persistence until 
mastery is gained is of incomparable value in all subsequent 
work. And the opposite is true; if the pupil is permitted to 
be careless and imperfect in his lessons, it is a habit that is 
likely never to be overcome. 

2G. Historical Recreations. — Every one that went to 
school three or four decades ago will remember the delight 
with which the announcement of a "spelling match" was 
received. Even yet a spelling match is almost as popular in 
the West as is baseball. This method has been extended to 
geography. In much the same way as in spelling, the pupils 
are tested in geographical knowledge. The writer has seen 
many competitive tests of this same kind in history. Several 
of our school textbooks contain extensive lists of questions 
intended to be used for this purpose. They may be given 
either as a miscellaneous review of an entire class, when any 
one may answer that can, or as is done in spelling, sides may 
be chosen and their comparative knowledge ascertained. 

The following questions for this purpose are copied for the 
sake of illustration: 



26 PEDAGOGICS OF HISTORY. § 6 

1. In what battle was "Betty Stark" the watchword ? 

2. What battles have resulted in the destruction or surrender of an 
entire army ? 

3. What general rushed into battle without orders and won it ? 

4. What trees are celebrated in our history ? 

5. What three ex-Presidents died on the 4th of July ? 

6. Give the coincidences in the lives of Webster, Clay, and Calhoun. 

7. What celebrated philosopher, when a boy, in order to buy books, 
went without meat ? 

The teacher must remember that these diversions must not 
be substituted for serious and genuine work in history. They 
are useful for creating an interest in, and for breaking the 
monotony of, the regular lessons; in short, they are used in 
the same way and for the same purpose as the spelling- 
matches of years ago. 

The pleasitre they give and the interest they arouse should 
suggest a general principle of success in teaching: Do not 
for long pursue the same method — seek variety, freshness, 
originality. 



METHODOLOGT. 



desciiiptio:n^ of tiif a arioits methods of 
teaching history. 

3*7. Any Method I^sed Exclusively lieoomes Monot- 
onous. — There is a strong human instinct for variety. We 
weary of the people that tell us over and over again the 
same stories, of the musicians whose music is always written 
in one key, and of the poets that always compose in the same 
meter. This repugnance to monotony is found also in 
children. Like their elders, they yearn for novelty. If 
required to sing at school the same song every morning, 
they soon become tired of it, however beautiful it may be. 
Hence, the teacher that wishes to make school a place of 
constant enjoyment to his pupils, must keep oitt of the ruts; 
he must be fertile in devices, and able to repeat as often as 



§ 6 PEDAGOGICS OF HISTORY. 27 

may be necessary, without becoming" monotonous. If he is 
content to assign lessons and to hear them recited always in 
accordance with a fixed method of procedure, he will soon 
have the mortification of hearing that his pupils like neither 
liim nor the school, of seeing an increase in their percentage 
of absenteeism, and of having their number depleted by 
many leaving school altogether. The fact is, there is no 
place in the world where a child can experience so much 
happiness as in a school properly conducted. The teacher of 
such a school must not only be original, resourceful, schol- 
arly, sympathetic, genial, and kindly, but he must also be 
familiar with the best and most approved methods. 

38. Many Methods of I'rocediire iii History. — Every 
school subject is susceptible of various methods of presenta- 
tion, and the effectiveness of each method depends 'upon 
many conditions, most of which have been mentioned under 
preceding topics. One of these conditions is that the teacher 
must thoroughly know the different methods and devices 
and be able to decide under what circumstances each should 
be employed. 

The writer, therefore, will proceed to explain the several 
plans that are employed in teaching history, and to make 
such comments upon them as may seem necessary. In doing 
this, he will describe with special minuteness the method 
that has proved so successful in Germany — the Laboratory 
methocl, which is being introduced more and more widely in 
the schools of this country. 

39. The Catechetical Method. — The oldest and most 
natural method of conducting a recitation is the Catechetical. 
In this the teacher asks questions and the -pupil answers 
them, if he can. This was a favorite method with Socrates, 
whose practice was to feign ignorance of some matter sup- 
posed to be thoroughly understood by his antagonist in 
argument. vSocrates would ask innumerable questions that 
the person questioned would answer in the unguarded way 
that comes from the conviction of having perfect knowledge 
of a subject; and presently the wily old philosopher would 



2S PEDAGOGICS OF HLSTORY. § G 

confront his opponent with a series of answers that were 
inconsistent with one another and ask him to reconcile them. 
From this practice of Socrates, there came into the Greek 
language a noun derived from the verb e'ipsLv, circin^ to speak. 
This word eironeia, means a dissembling, the asking of ques- 
tions that involve a snare. From the same source came the 
noun e'ipcov, e'lroj/, a dissembler, one that affects ignorance and 
says less than he thinks; finally we have in our own language 
the word irony. Every teacher has heard of the Socratic 
method, which is nearly synonymous with the Catecheti- 
cal method; but perhaps no other person ever employed 
the method of questioning so skilfully as did that wise 
old teacher. 

The catcc/iisj/is that counted for so much in the religious 
teaching of a half century ago were so called because they 
were made up of questions with answers. The first notions 
of what a textbook on history, geography, and many other 
subjects should be, required that it should take the cate- 
chetical form; and even yet we find such books in our 
schools. Many teachers continue to follow the plan of ques- 
tion and answer in conducting recitations. "■ Who discovered 
America?" "Columbus." " In what year ? " "In 1-192." 
Often, too, the question of the teacher is so constructed that 
it may be answered by jcs or no. Of course, all this is very 
bad ; so much so, that the Catechetical method has for a long 
time been practically abandoned in the making of textbooks, 
and to a degree in the recitations of pupils. 

And yet the art of skilful questioning is indispensable to 
the highest success in teaching. It is a practice among 
teachers to explain points that are not understood. "Sit 
erect and be attentive while I explain this difficulty," the 
teacher says, and immediately the class assumes an attitude 
of respectful attention, with ears for the most part hermet- 
ically sealed. But if the teacher clears away the difficulty 
by a series of questions in proper sequence, or, better still, 
if he delegates to some bright pupil the task of asking the 
questions necessary to lead a slow pupil to an understanding 
of the subject, the attention will be real and not feigned. 



gG PEDAGOGICS OF HISTORY. 21) 

A skilful lawyer cares less for the direct testimony of a 
witness than for what can be elicited by cross-examination. 
Indeed, the eminence of a lawyer is dependent more upon his 
expertness in the art of questioning than upon anything else. 
In like manner, no teacher deficient in this art can attain to 
the highest excellence in his profession. To use the Cate- 
chetical method with effect in teaching requires that the 
teacher shall himself thoroughly understand the subject 
imder consideration, and that he shall know the condition 
of the pupil's mind with respect to points not entirely com- 
prehended. The teacher must have, too, a sense of logical 
order that will enable him to construct a chain of questions 
in perfect sequence, leading the pupil from those points that 
he knows to those that he has failed U) grasp. 

Many books have been written about the art of question- 
ing, but this is something that cannot be learned from rules. 
The conditions of expertness in this art are indicated above 
— a perfect knowledge of the subject, of the end to be 
attained in any given case, and a strong sense of logical 
sequence. To these may be added such skill in the use of 
language as will enable the teacher to frame questions that 
are brief, suggestive, to the point, and without ambiguity. 

One of the most effective methods of making a recitation 
interesting is to require one pupil to ask a series of questions 
intended to lead another pupil to the comprehension of some 
point not thoroughly mastered, and to constitute the rest of 
the class as critics of the questions and their arrangement. 
The writer has witnessed recitations, the m< st exciting and 
interesting that could be conceived, conducted in this way, 
and during them the teacher rarely spoke. It would be 
difficult to exaggerate the value of skilful questioning as an 
auxiliary in the management of a recitation. vSuccess in this 
matter may not attend the first efforts of a teacher, but it 
will come later as a reward of experiment, patience, and 
reflection. 

30. Tlic Memoi'iteT Metliort of Stiidy and Recita- 
tion. — In this method the student commits to memorv the 



:30 PEDAGOGICS OF HISTORY. § G 

exact text of the author, and in recitation gives it as he 
learned it. Tlie objections to this are so numerous and so 
obvious that our best teachers have long ago abandoned it. 
Even yet, however, one does not need to go far to find this 
plan in use. In our large cities, where it might be expected 
that a practice so ruinous and antiquated would not be 
followed, it is still in vogue, and this will doubtless continue 
to be the case until all teachers are required to prepare for 
their work by professional training. It has been argued in 
favor of the Memoriter method that it cultivates the memory. 
But this argument is fallacious. When poetry or striking 
passages of prose are memorized, and are remembered on 
accoimt of their beauty, the effect is to train the memory; 
but it is well known that lessons in history are very soon 
forgotten. However carefully they are learned, they soon 
run into confusion in the mind and are forgotten. In this 
method, the words are everything and the thought nothing. 
It follows, therefore, that when the words are forgotten, 
nothing remains except a vague sense of half-defined images. 
Only such matters as are indispensable in our daily employ- 
ment, and are for that reason of frequent recurrence, are 
permanently fixed in our minds. The actor remembers his 
part in a play by virtue of repetition, but he reads the news- 
papers and speedily forgets what he has read. A poem full 
of beauty, emotion, and true to nature, is easily remembered, 
but a magazine article or an item in a newspaper makes but 
a slight impression upon the mind. The memory is very 
much like a servant. If discipline is relaxed, the servant 
becomes negligent and careless. If, on the contrary, he is 
held strictly to his responsibilities, he becomes more and 
more exact and painstaking. In like manner, if the memory 
is rigorously required to reproduce upon demand whatever 
has been confided to it, and, in case of failure, is punished by 
the imposition of additional tasks, it will in time become 
faithful and reliable. 

It must not be understood that the writer is opposed to 
verbatim memorizing, for the contrary is true. It is only 
with respect to the matter that is required to be committed 



§ (i PEDAGOGICS OF HISTORY. 3i 

to memory that objection is here made. The ideas in a 
historical textbook, but not the language, should be learned 
so carefully as never to be forgotten. The teacher, on the 
day before a lesson is to be recited, should go over it with 
the class. The objects in view should be to clear away any 
obscurity in' respect to the meaning, and to get an outline or 
analysis of the lesson. If it can be done, there should be 
found for each paragraph a single word that will recall its 
contents. This outline should be thoroughly fixed in the 
memory, and later, by way of review, it should be incor- 
porated with the outlines of preceding lessons, so as to form 
one continuous whole. During recitations, these outlines 
singly, and in order collectively, should frequently be called 
for, so that, when the textbook has been finished, its entire 
contents may be given by points from memory. 

Above all, do not permit pupils to give the exact text. 
One of the best exercises in acquiring and confirming a good 
stock of words is in the requirement that pupils shall give 
the author's thought in words of their own choosing. Ideas 
are easily remembered, but mere words are inevitably for- 
gotten. 

31. The Topical McMiod. — The term topical refers 
both to the division of the matter in a textbook, and also to 
one of the best methods of giving that subject matter in 
recitation. Nearly all school books of the present time have 
their contents broken up, and the topics indicated by con- 
.spicuous side heads. This facilitates the work, not only of 
the pupil, but also of the teacher. Of coin-se the topics 
should be in close logical connection, and upon this depends 
greatly the superiority of one maniial over another. The 
pupil should have these topics in his mind in their order of 
occurrence, and when called upon to recite, should be 
required to proceed without help from the teacher. Very 
frequently, two or more pupils may be designated to recite 
in turn the portions that make up a topic, if it is long and is 
divisible into parts. As has been stated above, the aiithor's 
language should in no case be given by the pupil. An 



32 PEDAGOGICS OF HISTORY. § 6 

outline of the day's lesson in conjunction with the preceding- 
lesson should be given by the first pupil that recites. Many 
teachers cause such an outline or analysis to be given both at 
the beginning and at the end of the lesson. The practice is 
a good one, and is worthy of general adoption. One very 
great advantage of this topical method is that a sense of 
logical sequence is developed among pupils. More than 
anything else, it is this art of properly dividing a subject 
into related parts that gives so great a charm to the writings 
of Macaulay. He was perhaps the greatest master of para- 
graphing that ever wrote in any language. Every paragraph 
is complete in itself and perfect; and the transition from one 
to another is graceful, and the sequence natural and obvious. 
It must not be understood that the Topical method pre- 
vents the employment at the same time of the Catechetical 
or the Memoriter method. If a teacher desires to analyze 
motives, or causes, or consequences; in short, if he teaches 
not history merely, but the philosophy of history, he must 
ask questions. This may be done as occasion arises during 
the progress of the recitation, or at its close. Which plan is 
the better must be determined in any given case by the 
teacher himself. But while it is sometimes necessary and 
advantageous to use the method of questioning, the Memori- 
ter method is invariably and hopelessly bad. When the 
questions of the teacher lead quickly and naturally to free 
and earnest discussion on the part of the pupils, the interest 
and profit will be very great. When the teacher of history 
can skilfully combine all the various methods and devices for 
awakening interest and enthusiasm among the pupils, we 
shall no longer hear it said that pupils hate the subject. No 
other subject is quite so fascinating as this, if it be well 
taught, but to teach it so as to secure the best results is very 
difficult. To prepare and deliver effectively a sermon or an 
oration is perhaps an easier task. 

33. Extension of Meaning' of tire Term "Topical." 

Although the word topical is usually employed in the 
sense explained under the preceding- head, there is another 



§ G PEDAGOGICS OF HISTORY. 33 

meaning' sometimes attached to it. This can best be illus- 
trated by a quotation from a brief outline by Professor Tyler 
of the historical work pursued under his direction at Cornell 
University : 

" Perhaps it may be a peculiarity in my work as a teacher of history 
that I am here permitted to give my whole attention to American 
history. At any rate, this fact enables me to organize the work of 
American history so as to cover, more perfectly than I could otherwise 
do, the whole field, from the prehistoric times of this continent down 
to the present, with a minuteness of attention var3-ing, of course, as the 
importance of the particular topic varies. I confess that I adopt for 
American history the principle which Professor Seeley, of Cambridge, 
is fond of applying to English history, namel^^ that while history 
should be thoroughly scientific in its method, its object should be prac- 
tical. To this extent, I believe in history with a tendency. My inter- 
est in our own past is derived chiefly from my interest in our own 
present and future ; and I teach American history, not so much to make 
historians, as to make citizens and good leaders for the state and 
nation. From this point of view, I decide upon the selection of liis- 
torical topics for special study. At present I should describe them as 
the following: 

" The Native Races, especially the Mound Builders and the North 
American Indians. 

" The alleged Pre-Columbian Discoveries. 

" The Origin and Enforcement of England's Claim to North America, 
as against Competing European Nations. 

"The Motives and Methods of English Colony Planting in America 
in the Seventeenth and Eighteenth Centuries. 

" The Development of Ideas and Institutions in the American Col)- 
nies, with Particular Reference to Religion, Education, Industry, and 
Civil Freedom. 

"The Grounds of Intercolonial Isolation and of Intercolonial Fellow- 
ship. 

" The History of the Formation of the National Constitution. 

" The Origin and Growth of Political Parties under the Constitution. 

"The History of Slavery as a Factor in American Politics, Culmina- 
ting in the Civil War of 1861-65. 

" In all these subjects, I try to generate and preserve in myself and 
my pupils such an anxiety for the truth, that we shall prefer it even to 
national traditions or the idolatries of party." 

33. Ttcmarks on the ?\)i"Cj>:oinj>'. — -The student will 
perceive that in the sense illustrated above, by the Topical 



34 PEDAGOGICS OF HISTORY. § 

method is meant no more than an arrangement in chrono- 
logical sequence of the principal items making up the com- 
plete history of a particular period. With this meaning, the 
method determines the arrangement of tlie contents of every 
scientific treatise on history. When the subdivisions are made 
down to minute epiijodes, the Topical method may be utilized 
in studying and reciting lessons from day to day, as lias 
already been explained. 

When, in the succession of general topics, the order of time 
is not followed, we have the Laboratory method, which is 
employed in the lycca and the universities of Germany, and 
in some of the colleges of the United States. Original 
researches by this latter method should be dominated by the 
Topical method, both in generalities and in particulars. 

i}4. The Ijaboi'ator.v Motliod. — In the teaching of 
chemistry, physics, mineralogy, metallurgy, botany, or any 
otiicr of the natural sciences, the need of a well e(iuip])cd 
laboratory is conceded. These laboratories, when comi)lete, 
are furni.shed with all necessary scientific instruments, books 
of reference, specimens, and everything that is re(|uired in 
the most exhaustive original investigations and experiments. 
Something of the kind has been proposed in the .study of 
history. Of cour.se, no instrumental aids are reciuiretl, but 
the plan contemplates that the student shall have access to 
all the original authorities, documents, reports, pamphlets, 
etc., that are resorted to by aiT ;uithor engaged in coni])iling 
a liistorical work. It is clear, however, that the unaided 
search of an ordinary student would yield nothing of value. 
He must have the guidance of a textbook from which he 
may learn where to find the information that he needs. 
vSuch books have been made in this country, l)ut they have 
not been used to any great extent. The plan presui)]:)oses 
an immense lil)rary accessible to the student. In this coun- 
try, even imder such circumstances, the method is not a good 
one. In this busy age, we cannot give to any one subject 
the time neees.sary to. make any such method successful. No 
one here desires to make a life work of the study of history, 



§6 PEDAGOGICS OF HISTORY. 35 

as is done in Germany, and in preparing to earn a livelihood, 
the most profound knowledge of this subject would rarely 
have any considerable market value in the United States. In 
Germany much is made of the study of history, and there is 
a demand for the services of persons specially trained to 
teach it. The Laboratory method proceeds upon the 
assumption that no modern writer of history is to be believed, 
and that every statement must be verified by reference to 
original sources. This, of course, takes more time than, in 
justice to other subjects of study, can be granted. Unless 
the student makes a life work of this subject, the Laboratory 
method is wholly impracticable as a plaii for the classroom. 
In the composition of a historical treatise, however, this is 
the only rational method of doing the work, and it is specially 
suited to the preparation of a dissertation on some particular 
historical topic, or controverted point. 

35. Historical Clubs. — In Germany especially, and to 
some extent in France, clubs for historical study are in 
vogue. They are commonly presided over by a professor 
or by some one designated for the pur|V)se. He assigns to 
each member a topic upon which to prepare a paper, and 
this, at a time specified, the writer reads before the club. 
Some one is chosen beforehand to criticize the contents of 
the paper. In order that the critic may be able to do his 
work thoroughly, he is permitted to examine the dissertation 
in advance. After the critic selected has been heard, other 
members follow. In the (ierman Gcscllscliaftcii these 
criticisms are unsparing, and appear to be made without any 
regard for the author's feelings. To an American the criti- 
cisms appear brutally blunt and severe, but they are accepted 
by the victim with an admirable philosophy and good nature. 
It is a valuable discipline, for nothing else so effectively 
enables one to avoid the folly of overestimating his own 
powers. 

Of course, it is not history alone that may be studied in 
this way. In every civilized country, there are innumerable 
organizations for various purposes, l)ut it is only in Germany 



30 PEDAGOGICS OF HISTORY. § 

since 1830, and in France for about a quarter of a century, 
that history has been systematically pursued by such societies. 
Much may be accomplished in this way, and the teacher in 
our public schools is better situated than any one else to 
inaugurate and direct the work. The teacher is naturally 
expected to take the initiative in such matters, particu- 
larly because he has perfect facilities for reaching parents 
and others whose cooperation is necessary. Indeed, the 
teacher's usefulness is not limited to his work in the class- 
room ; at least it should not be. When it is remembered that 
man is naturally a gregarious animal, and lends himself 
gladly to the furtherance of any scheme involving association 
with his fellows, we can readily see how useful an intelligent 
teacher, having executive and organizing aptitudes, may be 
in a community. Such activity greatly helps the teacher in 
his proper work in the schoolroom. It causes him to be bet- 
ter known and appreciated by the patrons of his school, and 
largely increases his influence. If such outside usefulness 
were generally prepared for in the schools where our teachers 
are trained, and the methods of its successful realization 
were carefully considered and systematized, the remrmera- 
tion and tenure of office of the profession would be speedily 
advanced. 

36. Intei'ost in IlistoTieal Study May Be Increased 
l>y Public Ijibravians. — An admirable plan of creating 
among the reading public an interest in historical reading 
and study has been described by Mr. William E. Foster, the 
Librarian of the Providence Public Library. The object in 
view included not only historical reading, but also such 
geographical, political, economical, and other subjects as are 
suggested by current events. The method pursued was to 
post at the library, newspaper clippings referring to impor- 
tant matters, and then to give below the titles and library 
numbers of books in which could be found additional infor- 
mation relating to the subjects so posted. It was immedi- 
ately found that the plan Avas an excellent one. Increasing 
numbers of visitors would stop to read the clippings, and, 



§ PEDA(U:)(;iCS OF HISTORY. 37 

naturally, they would procure and read the books. Neighbor- 
ing- educational institutions were invited to send lists of sub- 
jects in which their students were interested, and the volumes 
in which these subjects were treated were not only reported 
back, but the lists were posted at the library. The work 
was at first done by hectograph, but it was speedily necessary 
to resort to printing, and lists were finally sent to other cities. 
These lists were printed in the local newspapers whose read- 
ers would cut them out, take them along to the library to 
guide in the selection of books, and preserve them for future 
reference. Mr. Foster says that the plan developed until, 
in response to numerous requests, the more extended lists 
were printed in the " Library Journal " of New York, and 
that finally, in 1881, was begun the regular issue of the 
"Monthly Reference Lists." This latter periodical has 
attained a wide circulation in this country, and it has readers 
in Europe. He gives, as specimens of current topics, such as: 

"The Stability of the French Republic." 

"The German Empire." 

" European Interests in Egypt." 

" Indian Tribes in the United vStates." 

" The Unification of Italy." 

"The Closing Years of the Roman Republic." 

"The Plantagenets in England." 

"Tendencies of Local Self-Government in the United vStates." 

"Elements of Unity in Southeastern Europe." 

The foregoing is perhaps the nearest approach to the 
Laboratory method of Germany that is practicable in this 
country. Its tendency is to render the reading by the public 
systematic and orderly, and to turn it more to those subjects 
that at the time are uppermost in the public mind. It is, 
moreover, a plan by which intelligent students can be useful 
to others. There are many newspaper editors that would be 
glad to print such lists of topics, whether supplied by libra- 
rians or by well informed general readers. We hear much 
of altruistic effort; here is a field for persons disposed to 
exert themselves in behalf of a larger general intelligence. 
By these and similar means, the teacher may extend his 
influence and usefulness bevond the classroom. 



;3S PEDAGOGICS OF HISTORY. § (5 

37. The liectiire Metliod. — This method is much 
employed in the teaching of a great variety of subjects, 
particularly in colleges and universities, and in the higher 
technical institutions. This is more especially the case in 
the colleges and universities of Europe. During winter, in 
the United vStatcs, courses of lectures are very commonly 
arranged in nearly all of our large cities and towns. In 
these courses, the subjects are usually popular rather than 
didactic; for, if a lecture is intended to instruct, it is almost 
certain to be sparsely attended. The people that go to lec- 
tures expect to be entertained; a fact indicating that the 
Lecture method in teaching history has, under ordinary 
conditions, very little value. Unless a lecturer thoroughly 
knows his subject, and has, besides, rare graces of delivery, 
he cannot hope to furni.sh his audience any material or last- 
ing benefit. But there are circumstances imder which this 
method may be employed with excellent results by the 
teacher of history. Some of these conditions are as follows: 

1. TJic lecturer must be thoroughly master of his subject. — 
He must know the entire field covered by the lecture; he 
must know it not merely as a detail of facts — it must lie in 
his mind as scientific organized knowledge. Its philosophy 
miist be familiar to him. The laws of cause and effect, of 
sequence in time, and all the various interdependences must 
unite this knowledge into (Mie logical structure. Some one 
says that history is philosophy teaching by example. We 
can know onl_y facts and their relations ; but a knowledge of 
facts alone, facts in isolation, is scarcely worthy of being 
called knowledge. Facts become important only when their 
relations are fully understood. The voyage of Columl)us, 
considered merely as a voyage, has no more interest than 
any other voyage across the Atlantic; but when it is taken 
in connection with related events before and after, it becomes 
one of the most momentous occurrences in history. The 
battle between the Monitor and the Merrimac was a slight 
affair compared with the battle between the Chinese and the 
Japanese at the Yalu River, or the destruction of the Spanish 
fleet by Admiral Dewey in the harbor of Manila, or that of 



§ G PEDAGOGICS OF HLSTORV. 31) 

Admiral Cervcra at vSantiago clc Cuba. I^ut when that fh-st 
meeting- between iron vessels is considered in regard not only 
to its influence in shaping events during our own war, but 
also as necessitating the remodeling of the navies of the 
world, its deep significance becomes apparent. The per- 
formance of the dynamite cruiser "Vesuvius" at Santiago de 
Cuba, and the late developments in the matter of snbmarine 
navigation, will doubtless l)e the beginning of striking- 
readjustments of the world's methods of warfare. The great- 
ness of events, therefore, depends not so much on themselves 
as on their relations to other events. 

It folknvs, theref(n-e, that to employ the Lecture method 
effectively in teaching history, it is necessary for the lec- 
turer to have mastered the philosophy of his subject, to have 
pondered deeply upon the logic of events. His knowledge 
must be thorough and profound, and it must be organized. 
He must be able to give in a sentence what may have cost 
him weeks of reading and reflection. 

2. He must not oitcr into details. — If the lecturer intro- 
duces many particulars, it becomes impossil)le for him to 
exhibit strongly any logical and connected whole. By the 
lecturer's matter and manner, his audience should be com- 
pelled to grasp and remember the general scheme of the 
lecture. This scheme should be so conceived and presented 
as to create an impulse on the part of the audience to find 
the details that will confirm and com])lete it. It should l)e 
a nucleus aroimd which tlicre shall be a continuous accumu- 
lation. 

3. 'flic stndoit should be supplied toitlt a "vod outline of 
the lecture. — It is customary for students to take notes of 
lectiu'es that they deem important. If original research with 
reference to the matters treated is contciiiplated, these are 
indispensable. But the task of writing these notes diverts 
the attention from the main argument, and much of the 
effect and unity is lost. The best method of meeting this 
requirement is for the lecturer himself to supply a complete 
outline of the lecture. By this means he avoids the possi- 
bility of being misunderstood, and tlie later researches of the 



40 PEDAGOGICvS OF HISTORY. § G 

students are perfectly definite. If reference is made in these 
notes to authorities where details may be found, the outline 
of the lecture becomes immensely more valuable. In any 
case, the notes can be made the ba.sis for subsequent exami- 
nation into the proficiency of the students. This is the 
method of procedure in our schools of law and medicine, 
where the teaching is largely done by means of lectures. 

38. Ileiuai'ks on the Ijectvire Metliotl. — ^In teaching 
history by this method, great care is necessary that the sub- 
ject and its treatment shall be adapted to the age and intelli- 
gence of the pupils. This is a matter of difficulty. It 
requires a tliorough knowledge b}- the lecturer of the mental 
status of the pupils, and besides, that he shall have the 
I'ather rare versatility that enables one to make his language, 
manner, and method suit an audience of children or of cul- 
tured adults. Tyndall possessed this power of adaptation 
to a wonderful degree. His Christmas lectures on Light 
and Electricity were listened to with rapt attention by audi- 
ences of more than 5,000 children, and in this country he 
lectured on the same subjects to immense audiences com- 
posed largely of educated people and specialists. The error 
into which a lecturer is inost likely to fall will consist, there- 
fore, in making his subject too little philosophical, or too 
profoundly so. 

If a discussion of the lecture is made to follow, directed 
and supplemented by the lecturer himself, its effect is ampli- 
fied and deepened, and erroneous impressions corrected. In 
German)^, this method, with various accompaniments and 
modifications, and in its most elaborate and philosophical 
form, is much employed in the Seminar ia or "Training 
Schools," and in the "Practice Course " of the universities. 
But it is to be remembered that, in these departments, 
only comparatively small groups of advanced students are 
addressed, and that the lecture is intended only to suggest 
lines of subsequent original research by the students. 

It is extremely doubtful whether the most accomplished 
lecturer on history proper could make this method valuable 



§ G PEDAGOGICvS OF HISTORY. 41 

below our high schools. Into these, however, and into our 
colleges, it has been introduced, and in many cases with 
marked success. But while this method is useful only in 
the higher study of history, there is a modification of it that 
may be regarded as indispensable in the historical work in 
our lower schools. This, on account of its importance, shall 
be carefully explained in the next topic. 

39. The liiograpliical Method. — Before history proper 
can be studied with any profit from textbooks, the historic 
sense must be developed; and of all methods for this pur- 
pose, the Biographical method is the best with beginners. 
By the historic sense is meant: 

1. A demand of the uiind that narratives sJiall be distin- 
guished as time or as mere myth or story. — To very young 
children a fairy story is as apparently true as the account 
of a real occurrence. The tales of the "Arabian Nights" 
arc just as veracious to them as if the incidents occurred 
before their own eyes. Dickens strikingly exemplifies this 
in a beautiful sketch, entitled "The Child's Story": 

" They had plenty of the finest toys in the world, and the most 
astonishing picture books — all about simitars and slippers and turbans, 
and dwarfs and giants, and genii and fairies, and bluebeards and 
beanstalks, and riches and caverns and forests, and Valentines and 
Orsons; and all new and all tr-itc." 

Indeed, it never occurs to children up to about eight years 
of age to inquire as to the truth of what they hear or read — 
everything is real, everything true. At this age, questions 
of probability begin feebly to suggest themselves, and the 
mind begins to file, but, with slight emphasis, its protests 
against incongruity. 

As the result of many tests inade upon children, it has 
been ascertained that by certain kinds of training this sense 
of historic truth may be rapidly developed, and thus the 
child may be prepared for serious historical work. It would 
be interesting to detail here some of the many tests that 
have revealed this psychological fact, but the limits assigned 
for this Paper will not permit it. 



42 PEDAGOGICS OF HISTORY. § G 

2. A demand of the mind for tlic time of events. — 
What some one has called t\\Q perspective of In story is absent 
in young children. The writers of fairy stories have never 
deemed it necessary to be more specific in this respect than 
to begin with " Once upon a time," or with " Once upon a 
time, long, long ago," or with similar vague phrases. To 
young children, the stories of Columbus and Washington are 
equally remote, and neither dates farther back or forward 
than " King Arthur's Round Table," or the myth of " Jason 
and the Golden Fleece." No such inquir}^ as "When did it 
all happen ? " is heard from these youthful auditors until 
after about the age of eight years has been passed. After this 
time, the demand for the time of events is made with 
increasing frequency. vStill later, comes the mental require- 
inent for a definite sequence in regard to time of the several 
items that make up a single event; and still later, for the 
relation in time of several independent events. Until this 
last instinct has become definite, the historic sense with 
respect to time is incomplete. And it is long after the 
pupil desires to know the sequence of time in the events of 
a narrative that he becomes importunate alwut what was at 
the same time going on in the rest of the world. 

3. A mental demand for the cause and the conse- 
quence of historic action. — Early in the life of children 
we often hear the inquir)^, "Why did you do that ? " This 
is one of the first manifestations of an instinct to investigate 
the causes of action. Such investigations are at first con- 
fined to the child's actual surroundings, and they generally 
have reference only to actions that affect his own physical or 
mental well being, or his personal rights. It is much later 
when he carries these inquiries outside into the matters of 
history. In these early years, his instinct deals only with 
the causes, not the consequences, of personal actions. Long 
afterwards the tendency asserts itself to trace action to the 
effect it produces. 

It is related that a lawyer once advertised for an office boy. 
On the day indicated, a large number of applicants appeared. 
The lawyer said, " Boys, before I decide which one of you I 



§ 6 PEDAGOGICS OF HLSTORY. 43 

shall select, I wish to tell you a story. " He then very vividly, 
as some lawyers can, related an incident that may be out- 
lined as follows : 

"A farmer one night heard a disturbance near his barn 
among- his pcoultry — with his gun, he went to the barn — an 
owl sat on the roof — the farmer shot at it — the wad from his 
gun lodged among the dry shingles and fired the barn — it 
burned rapidly — his horses and cows were in the barn — he 
attempted to save them — his life was lost in the effort — his 
wife, in trying to rescue her husband, was burned to death — the 
barn, the farmer, his wife, and all the stock were consumed." 

The boys listened with suspended breath, and a deep sigh 
at the close told the story of the intensity of their interest 
and sympathy. Presently one of them asked, " Mister, did 
he hit the owl ?" "You are the boy I want," answered the 
lawyer. In this is an illustration of the fact that the instinct 
to trace events to their legitimate outcome has a market 
value. Doubtless the student is familiar with the myth con- 
cerning Epimetheus and his brother Prometheus. Their 
names, denoting afterthought and forethought, are indicative 
of their mental qualities. Most people have Epimetheus, 
and very few, Prometheus, for their prototype. 

4. A;/ iinpnhc to criticize Jiistoric action, and to make 
inferences from it. — Criticisms of historic events generally 
have reference to the motives of action, and are based upon 
the assumption that actions have an ethical quality — right- 
ness or wrongness; or they concern the expediency of the 
means employed to accomplish certain ends. 

40. Ktliical Criticism. — To illustrate what is meant by 
ethical criticism, the incident may be cited of the slaughter, 
by order of Napoleon, of nearly 1,500 Turkish prisoners taken 
at the storming of Jaffa. His biographers and critics are 
still disputing whether the exigencies of the situation and the 
laws of war warranted the act. And the people of our own 
country are by no means unanimous on the question whether 
General Grant was right to "fight it out on this line if it 
takes all summer. " He had to choose between a more dilatory 



44 PEDAGOGICvS of HLSTORY. § 6 

method with a probable saving of life, and the method that 
he adopted, that of ending the war quickly by sheer force of 
superior numbers, and without considering the lives it might 
cost. Much is to be said on each side of such questions, and 
it is a part of the teacher's work to develop in his pupils 
a critical instinct that looks at historical events from all sides. 

To a child, the ethical quality in human deeds is quite 
overshadowed by heroic action and daring. The doings of 
the pirates of the Spanish seas create no sentiment of revolt- 
ing and horror; they are only fearless freebooters whose 
legitimate prey is the world. The horrors of battle are quite 
lost in the glorious exhilaration as he reads or hears of the 
rush of infantry, the thunder-like roar of artillery, and the 
magnificent charges of cavalry. There is no room in his 
young heart for pity of the vanquished, he cannot hear the 
groans of the wounded, or see the white iipturned faces of 
the dead. Very slow is the growth of the ethical sense. 
Even "children of larger growth" have a very rudimentary 
notion of the right and the wrong in human action. 

There is gradiially developed in every mind a disposition 
to predict or infej what is to happen next in any succession 
of events; or to conjecture the occurrences that have pre- 
ceded a given state of things. When Robinson Crusoe saw 
the strange footprint in the. sand, the remains of a fire, and 
the bones that he recognized as human, his first mental 
impulse was to seek an explanation of these phenomena. His 
earliest conclusion was that his island had human inhabitants 
other than himself. This he investigated and disproved, and 
thiis established the alternative fact that the island had been 
visited by cannibals. So far he had been making inferences 
as to what had already happened. Now he begins to deal 
with the ////// ;r. " They will return. What has happened 
is likely to happen again." Such is his thought, and from 
that time he is in daily expectation of their return. 

41. Test of the PoAvei* of Inference. — ^To test the 
power of inference in young students of history, Mary Sheldon 
Barnes gives the following as a typical exercise : 



§ G PEDAGOGICS OF HISTORY. 45 

" If you were shipwrecked on an island in the middle of the sea, and 
[if J you found in one corner of the island an old house of logs, and part 
of an old wooden boat with broken arrows in the bottom of it, what 
would these things tell you ?" 

Many children of different ages and degrees of intelligence 
were required to give their views in writing. Their infer- 
ences as to what had happened on the island were carefully 
collated, and some very instructive conclusions were reached 
regarding the development of the faculty of critical, legiti- 
mate, and historical inference at different school ages. The 
stitdent will find her little book, "Studies in Historical 
Method," to contain much suggestive and valuable help. 

4^. Method of Developing: tlie Historic Sense. — 

Having set forth pretty fully what is meant by the historic 
sciiSL\ we shall now explain what is generally conceded to be 
the best method of developing it. 

Nowhere in the world has history been so successfully 
, taught as in Germany. The subject is handled there in such 
a way as to make the student an intelligent and a persistent 
reader of history during his entire life. His training is such, 
too, that his subsequent reading is methodical and systematic. 
He is not taught to " hate history," but it is to him an 
inspiration and a discipline. With him the period of his- 
torical study preceding the university work covers about 
nine years — from the age of nine or ten to about nineteen. 
It is during the first five years that the Biographical method 
is employed. This method we now proceed to describe. 

The first two years of historical work are taken up with 
stories told by the teacher about the great men and the great 
events of the world. In this work no dates are given, and 
times are indicated only approximately. The central pur- 
pose is to awaken and develop the historic sense, and to this 
end, the impressions must be the most vivid possible. Only 
teachers specially trained are employed in this work. Of 
course no textbooks or books of any kind are used. It is 
much the same as the entertaining of children by telling 
them stories in the nursery. These stories occupy a half 



46 PEDAGOGICS OF HISTORY. § G 

hour each, t\\'4ce a week, and, naturally, they are eagerly 
anticipated by the pupils. They serve to carry the children 
from their own narrow sphere into the great world of heroic 
effort and achievement beyond, and to awaken vague ambi- 
tions and hopes concerning their own future. Every one 
knows the intense interest and delight that children find in a 
story well told, and no effect upon the mind endures as does 
that made during highly wrought emotion. Leonidas, 
"lion-like," becomes, to the child so taught, a type of heroic 
and unselfish devotion to country forevermore. Salamis — 
the heart of the child will beat faster hereafter when he hears 
the name. Themistocles, Aristides, Demosthenes, Lycurgus, 
Socrates, Alexander — what a mine of biographical wealth 
the old Greek race furnishes for the delectation of the stu- 
dent, and the ideals and aspirations of men are higher and 
nobler for the lives of such men. 

In these tales, the teacher naturally begins with his own 
country, and proceeds in an orderly way with the epoch- 
making men and events of other countries. Gradually, as 
the horizon of the pupil widens, he comes to feel the need of 
greater definiteness as to time and place, cause and effect, 
ethical fitness, and means and motives. Geography lends 
its aid. " Here was born this great man; here he did his 
work; here he died and was buried." "On the banks of this 
river the battle was fought; here, through a mountain pass 
the defeated army attempted to escape and was destroyed or 
captured." Little by little, pity for the vanquished and for 
the subsequent fate of those whose fiiture was ruined by the 
defeat, begins to take its place in the child's heart, and 
questions of right and wrong — the ethical sense — are vaguely 
outlined in his consciousness. 

And, thus, slowly indeed, but surely, is built up a mental 
substructiu-e upon which shall rest later a symmetrical 
knowledge of history. 

At the end of two yeans, the same ground is gone over 
again, but in a different way. The Biographical method is 
still pursued, but this time the object is to link events into 
a harmonious outline. The elements of time and place, of 



§ <j PEDAGOGICvS OF HISTORY. . 47 

cause and effect, of means and end, and of. ethical fitness 
are to be employed in g'iving unity of effect. The Battle of 
Salamis has already been told; now the whole story of 
Xerxes' invasion of Greece, with its causes and consequences, 
is gone over. The pupil is furnished with a pamphlet con- 
taining names and dates, not for study, but simply as sug- 
gestive aids to the memory. This pamphlet is prepared by 
the teacher, and the order of its contents is closely followed 
in his work. It is useful, too, in the oral and written 
exercises on the part of the pupils, who are rec^uired to 
impress upon their memories what has been taught. The 
law of association is utilized by every possible means. Brief, 
but clear explanations of the manners and customs that pre- 
vailed in those far-away historic times are given by the 
teacher; forms of government are described, not at length 
and formally, but in sharp, well defined outline. The learn- 
ing of dates under this regime is not the slavish work usually 
made of it, but each date takes its place in the memory 
easily, and stands with respect to other dates as definitely as 
a star in a constellation. The characters of whom he has 
learned are not mere names; they are clothed in flesh, and 
warm blood circulates through their veins and arteries. 
What Emerson says of science is true of history, " Some- 
thing is wanting to science imtil it has been humanized. 
The table of logarithms is one thing, and its vital play in 
botany, music, optics, and architecture, another." So these 
names of history must be changed into real personages in the 
mind of the pupil, before they become examples and imper- 
atives in his life. Mencius says, " A sage is the instructor 
of a hundred ages." When we get this realistic knowledge 
of the wise and the noble, we ourselves are made wiser and 
nobler. 

This, then, is the Biographical method, and its successful 
use depends almost entirely upon the teacher. He, must, of 
course, know his subject as an organized whole, as well as 
know it in its parts; he must be willing to devote much time 
to preparation; he must be able to produce vivid impres- 
sions; and he must not lose his grasp upon tlie general 



48 PEDAGOGICS OF HISTORY. § G 

scheme, and, in consequence, mutilate and weaken the parts 
by meaningless digressions. 

43. A Specimen Iiessoii in a Geruiaii Scliool. — The 

following account of a lesson illustrating the Biographical 
method is taken from Dr. Klemm : 

(1) A biographical narrative was given by the teacher, who spoke in 
very simple and appropriate language, but feelingly, with the glow of 
enthusiasm and the chest tone of conviction. He made each pupil 
identify himself with the hero of the story. The map was frequently 
used or referred to. Bits of poetry taken from the reader were inter- 
woven, and circumstances of our time, as well as persons of very recent 
history, were mentioned at the proper occasion. The attention was 
breathless. 

(2) The story was then repeated by pupils, who were now and then 
interrupted by leading questions. The answers were again used to 
develop new thoughts not brought out by the first narration. Particu- 
larly was it cause and effect, and the moral value of certain historical 
actions which claimed the attention of the teacher. To me it was very 
instructive to see these children search for analogous cases in human 
life as they knew it. 

(3) The pupils were led to search in their stores of historical knowl- 
edge for analogous cases, or cases of decided contrast. This gave me 
an insight into tlie extent of their knowledge. When, for instance, 
certain civil virtues were spoken of, they mentioned cases that revealed 
a very laudable familiarity with history. But all their knowledge had 
been grouped around a number of centers — that is, great men. That 
is to say, their knowledge had been gained through biographies. 

(4) The pupils were told to write, m connected narration, what they 
had just learned. This proved a fertile composition exercise, because 
the pupils had something to write about — a thing that is not quite so 
frequent in schools as seems desirable. 

44. Underlying: Principles of the Ijcsson. — Dr. 

Klemm goes on to tell of the teacher's explanation to him 
of the principles that should characterize the method : 

The aim should be "to nourish and strengthen all the powers of the 
soul, interest, emotion, and volition." "The pupil's intellect is 
increased by making him familiar with historical deeds, by affording 
comparisons and making distinctions, by causing keen judgment and 
correct conclusions." " The pupil's heart is influenced by instruction 
in history, because many great, sublime, noble, and beautiful actions 
and motives are presented, which cause pleasure, and lead to imitation, 



§ 6 PEDAGOGICS OF HISTORY. 49 

unconsciously to th'e pupil." " The pupil's will power is greatly stim- 
ulated by instruction in history, because he is warned and inspired by 
truth, right, and duty, to love his country and his fellow men." 

45. Metliods of Securing: These Ends. — The teacher 
enunciates to Dr. Kletnm the conditions upon which depends 
the securement of these ends, as follows: 

(1) That the teacher of history be a person whose heart is full of 
patriotism, and beats strongly for trvith, right, and duty. 

(3) That the instruction be not a mere recital of names and dates, 
of battles and acquisitions of land, nor dissertations upon abstract 
ideas and generalities, but above all, a simple narration of deeds and 
events, and a glowing description of persons and circumstances. 

(3) Tliat the teacher connect the new historical knowledge with 
circumstances and conditions, such as are either known to the pupils, 
or are near enough at hand to be drawn into the discussion. 

(4) That the pupil should not be allowed to remain receptive, but 
must be induced to be active in this study. 

(5) That the teacher should induce his pupils to compare similar 
and dissimilar actions and persons, and thereby induce judgment upon 
cause and effect from a moral or an ethical standpoint, so that not 
merely the intellect be developed, but also the heart and the will. 

(C) That instruction in history be brought into organic connection 
with the study of language; for this reason, reading is to be brought 
in as an assistant. Recitations of patriotic poems and ballads can 
be woven m prohtably, and that geography must aid history is self- 
evident. 

46. Remarks Upon the Foregoing Illnstrative 
Lesson. — The writer feels that it is unnecessary to apologize 
for illustrating- at length so excellent a plan as is realized in 
the Biographical method of beginning history. That the 
method is excellent is demonstrated by its long use in the 
German elementary schools. That it has not proved so val- 
uable in this country is owing, not to faults in the method 
itself, but to a lack of ability on the part of the teacher to 
use it skilfully and effectively. Educators know that if 
children have the good fortune to fall into the hands of able 
teachers, they themselves, should they subsequently become 
teachers, will remember and strive to imitate, in matter, 
manner, and method, their former teachers. And it is 
probably true that no person ever became a great teacher, if 



50 PEDAGOGICS OF HISTORY. § 

he himself had been poorly taught. Man is only an improved 
type of the ape in this imitative instinct. Many an excellent 
plan of procedure in teaching has been abandoned for no 
better reason than that the teacher lacked the genius to 
devise original methods of using it, and had no illustrative 
prototype. In teaching, as in other things, excellence is 
attained by the slow processes of evolution, and final success 
is hypothecated upon innumerable antecedent failures. 

47. The Biograpliieal Method as Advocated by 
Herbart and Others. — So marked have been the good 
results obtained in the German schools by this method, that 
many pedagogists, at whose head are Herbart and Ziller, 
have advocated its introduction at the beginning of the 
child's school life. They have outlined the course to be 
pursued in carrying out their theories. During the first 
year, certain of the tales of the Grimm Brothers are told 
over and over again by the teacher, and are finally drawn 
from the children as voluntary oral narrative, or by means 
of suggestive questions. These become the material for 
lessons in morals, religion, general information, object 
lessons, language lessons, etc. The delightful stories of 
Hans Christian Andersen, being slightly more realistic, can 
be similarly used. 

The second year's work consists of the story of Robinson 
Criisoe. This is broken up into brief episodes, each com-' 
plete in itself, and when, towards the close of the year, they 
are united, they form a connected whole. 

After this come the vSagas of the Scandinavian mythology, 
stories of Odin, Thor, Loki, Balder, the Valkyries, and of 
many others of the rugged but poetically beautiful characters 
that figure in the myths of the icy North. From these, too, 
are drawn lessons of poetic and moral bcaut-y, and they serve 
to furnish concrete images for the imaginative instinct found 
in every child. 

Then the stories of the Old Testament are utilized, followed 
by tales from the Odyssey and the Iliad, vShakespeare, Livy, 
Herodotus, Xenophon, Hesiod, ^schylus, and others. So 



§ 6 PEDAGOGICS OF MLSTORY. 51 

the work goes on to the time at which history proper is 
taken lip in the regular German course, when the pupil is 
nine or ten years of age. 

48. Some Reasons for Beginning History Early. — 

It is conceded among educators that the chief need with 
little children is language. In consequence of this fact, 
studied and systematic work has been instituted to provide 
for this want. The most conspicuous effort in this direction 
is the kindergarten, which has been much decried and much 
lauded. The central requirement of kindergarten work is 
that it shall deal with concrete objects, a knowledge of 
which reaches the mind principally through the two senses 
of sight and feeling. Almost nothing is done for the other 
senses; the child is expected to get, in his own environ- 
ment, all the sensations he rec^uires of smell, taste, and 
hearing. Of the words that he learns, the greater part 
are nouns and adjectives; the various actions and motions 
expressed by verbs he learns by observation, mostly else- 
where than in the kindergarten. Adverbs he learns with 
verbs, and the various relation words and the pronouns 
come but slowly. Now the teacher that tells him a fairy 
story, or a tale from mythology, must reach his mind with- 
out placing in his hands sensible objects of any kind. 
Verbs, adverbs, pronouns, relation words, all easy to be 
understood, and all illustrated by what the child sees every 
day, must be so used that, by sheer force of repetition and 
context, he may gradually get exact notions of their mean- 
ings, and learn to use them himself. In this early work, 
the value of a teacher is measured by his skill in story-tell- 
ing — by his ability to transfer to ideal uses words usually 
applied to sensible objects, by his vivacity, the music of his 
voice, and his earnestness. Obviously, teaching of this 
kind supplements the work among the concrete in the 
kindergarten, and rapidly supplies a vocabulary suitable to 
the narrow sphere of a child. If rightly done, it is an excel- 
lent training in the use of words in ideal or mental senses. 
Another imperative rec|uirement in the education of a 



52 PEDAGOGICS OF HISTORY. § 6 

young child is the formation in his mind of definite centers 
of interest that may, by subsequent accumulations, be 
enlarged and rendered more comprehensive and more 
definitely significant. There is a certain attractive affin- 
ity between such centers in memory and thought and the 
related ideas that reach the child later. "The child must 
have ideas before he can compare and classify them," say 
our educators. What better way to get ideas than this ? 

When we remember that, of the words with which we are 
familiar, only a very small percentage was learned from the 
dictionary, and that the others were gradually accumulated 
by reading and conversation alone, it will be obvious that the 
story-telling method is a correct natural method. It is a 
method that begins in the nursery and endures as long as we 
live. Some one says of the Biographical method that it 
matters but little how early it is begun, provided only that it 
is begun rightly. 

Many other reasons for this early work might be given, but 
enough has been said on the subject to show that it would be 
diffici:lt to begin too soon to enrich the vocabularies of our 
children, to awaken and develop the historic sense, and to 
form in their minds definite centers of historical interest. 

49. The Comparative Metliod. — Mr. Herbert B. 
Adams, one of our most eminent teachers of history, in 
describing this method, employs the word comparative in 
two senses. In its first use, he makes it signify a com- 
parison of similar phases of the history of different nations at 
the same or different times. A brief quotation from this 
author will illustrate : 

"It would be a fine thing for American students, if, in studying 
special topics in the history of their own country, they would occasion- 
ally compare the phases of historic truth here discovered with similar 
phases discovered elsewhere ; if, for example, the colonial beginnings 
of North America should be compared with Aryan migrations west- 
ward into Greece and Italy, or again with the colonial systems of Greece 
and of the Roman Empire, or of the English Empire today, which is 
continuing in South Africa and Australia and in Manitoba, the same 
old spirit of enterprise which colonized the Atlantic seaboard of North 



§ 6 PEDAGOGICS OF HLSTORY. 53 

America. It would interest young minds to have parallels drawn 
between English colonies, Grecian commonwealths, Roman provinces, 
the United Cantons of Switzerland, and the United States of Holland. 
To be sure, these various topics would require considerable study on 
the part of teacher and pupil, but the fathers of the American Constitu- 
tion, Madison, Hamilton, and others, went over such ground in prepar- 
ing the platform of our present federal government." 

It is this method that Pkitarch follows in his dclii.;htful 
"parallels." In all the range of biographical literature, 
there is nothing quite so fascinating as these parallels, and 
while this fact is due in large measure to the style in which 
they are written, in still larger measure it is owing to the 
pleasure we find in the comparison of similar characters, in 
the detection of differences and resemblances. This method 
is applicable in the study of innumerable phases of the his- 
tory of nations, as, for example, the comparison of otir own 
Civil War with the French Revolution or with the Revolution 
in England against the Stuarts under Cromwell ; the inva- 
sion of Greece by Xerxes, and the expedition of Alexander; 
the invasion of Russia by Napoleon and the March of the 
Ten Thousand under Xenophon; the commercial and naval 
rivalry between Rome and Carthage, and the similar rivalry 
between England and Continental Europe. The well 
informed and thoughtful teacher of history Avill have no 
difficulty in finding examples to illustrate almost any epi- 
sode in the history of this country. 

The second sense in which Professor Adams i;scs the 
term comparative will best be understood from the following 
quotation : 

" But my special plea is for the application of the Comparative 
method to the use of historical literature. Students should learn to 
view history in different lights and from various standpoints. Instead 
of relying passively upon the ipse di.xit of the schoolmaster, or of the 
school book, or of some one historian, pupils should learn to judge for 
themselves by comparing evidence. Of course, some discretion should 
be exercised by the teacher in the case of young pupils ; but even 
children are attracted by different versions of the same tale or legend, 
and catch at new points of interest with all the eagerness of original 
investigators. The scattered elements of fact or tradition should be 
brought together as children piece together the scattered blocks of a 



54 PEDAGOGICS OF HISTORY. § (i 

map. The criterion of all truth, as well as of all art, ia/t/ziess. Com- 
parison of different accounts of the same historic event would no more 
injure boys and girls than would a comparative study of the four 
gospels. On the contrary, such comparisons strengthen the judgment, 
and give it greater independence and stability. In teaching history, 
altogether too much stress has been laid, in many of our schools, upon 
mere forms of verbal expression in the textbook, as though historic 
truth consists in the repetition of what some author has said. It would 
be far better for the student to read the same story in several different 
form.^, and then to give his own version. The latter process would be 
an independent historical view based upon a variety of evidence. The 
memorizing of 'words, words,' prevents the assimilation of facts, and 
clogs the mental process of reflection and private judgment." 

50. Remarks on the Comparative Metliort. — It will 
be seen from the foregoing' quotations that Professor Adams 
employs the term comparative in two widely different mean- 
ings; one meaning denotes a comparison of analogous events, 
the other a comparison of different accounts of the same 
event. In the first, the trustworthiness of the historic records 
is assumed wherever they may be found , in the second, the 
truth or the completeness of the various accounts must be 
thought of as only approximate — the records are to be taken 
together and averaged. Each requires judgment and skill 
in collating resemblances and differences, but the former 
exercises and disciplines a higher and more mature phase 
of the faculty of comparison than does the latter, and both 
involve much study and reflection on the part of the pupils 
and the teacher. Under proper conditions of age and 
maturity of the pupils, of industry, intelligence, and scholar- 
ship on the part of the teacher, and of library facilities, this 
method woitld undoubtedly be very effective. But, unfortu- 
nately, these conditions of success are generally wanting, and 
this is especially the case in our lower grades of schools. 
Only to a very limited extent would this plan of history 
work be practicable in our country schools, and the same 
would be largely the case in the graded schools of our towns 
and cities. However, if the teacher himself is in possession 
of wide and accurate historic scholarship, and at the same 
time has access to the necessary historical authorities, both 



§ 6 PEDAGOGICS OF HISTORY. 55 

phases of the method may be advantaoconsly resorted to, both 
in country and in city schools. By reading different accounts 
of the same event to his pupils, emphasizing similarities and 
differences, by causing among them discussions that he di- 
rects and summarizes, and by many other means, the teacher 
may utilize, in a large measure, the Comparative method. 

51. Other Methods. — There are several other plans of 
teaching history that have been designated b}^ distinguishing 
names. These, however, are in use only in the higher insti- 
tutions of learning in this and other countries, and are, there- 
fore, of little practical value to the ordinary teacher of history. 
But while they may not be of any value as working methods, 
to the students of this Paper, they shall be briefly explained 
below; fen- teachers may perhaps find in them guiding sug- 
gestions for their own study of history, aud for the work of 
their pupils in other subjects. 

1. llie Cooperative Method. — This is a method not only 
of studying history, but of icriting it. The late Leopold 
von Ranke, perhaps the greatest of German historians, who 
did more than any one else to originate, develop, and organ- 
ize the historical methods of his country, is the father of the 
Cooperative method. 

"The most notable examjile of the Cooperative method in universal 
history, " says Professor Adams, "is the new monographic history of 
the world, edited by Professor Wilhehii Oncken, but composed by the 
eminent specialists in Germany. One man writes the history of Egypt 
in the light of modern research ; anotlier that of Persia; a third reviews 
the history of Greece, giving the latest results of Grecian archeological 
investigations; others revise Roman history and the early history of 
Germanic peoples." 

The foregoing extract will sufficiently illustrate what is 
involved in this method. In every department of human 
activity the division of labor has been introduced so generally 
that, in the ordinary industries, it is now difficult to find a 
"trade " that one may learn in its entirety. Manufacturers 
find that, in the construction of a whole composed of many 
parts, labor is economized and the output increased by 
assigning the various parts to as many different individuals. 



56 PEDAGOGICS OF HISTORY. § O 

Thus, one man makes, or partially makes, a certain wheel in 
a watch, another works upon a different wheel, and still 
another turns, engraves, or decorates the case. In this 
division of labor, aptitudes of different workers determine 
what each shall do. 

The same method has been carried into literary work. The 
making of a great dictionary is a good illustration. One 
specialist is eminent in physical science; to him is assigned 
the work of defining the terms belonging to that department. 
The most eminent authority obtainable for each department 
writes the definitions pertaining to his special subject. The 
whole is a great cooperative work. 

More than twenty-five years ago, the publishing house of 
D. Appleton & Co. began to issue, under the editorship of 
Professor Youmans, a list of popular science treatises called 
the "International Scientific Series." Each volume covered 
some special topic, and was written by the man supposed to 
be, as compared with all others, the most competent in the 
world to treat that particular subject. Professor Tyndall 
wrote the first volume, the title of which is " The Forms of 
Water." Other authors just as eminent followed, until this 
series, a perfect illustration of the Cooperative method, has 
grown into a collection of incomparable value. To know 
thoroughly the contents of all these works, would be an 
admirable general education in science for any man. 

2. Tlic Sciuinary MctJiod. — The Seminary method is only 
a continuation of the German plan of teaching history. It is 
distinguished by original research by the students, of whom 
a comparatively small number work together; by the prep- 
aration of original theses as the result of such investiga- 
tions; by the reading and criticism of these theses by students 
and teachers, and by the restriction within narrow limits of 
the areas investigated at any one time. 

" The Seminary method of modern universities is merely the develop- 
ment of the old scholastic method of advancing philosophical inquiry 
by the defense of original theses. The Seminary is still a training 
school [in Germany] for doctors of philosophy; but it has evolved from 
a nursery of dogma into a laboratory of scientific truth." — H. B. Adams. 



§ PEDAGOGICvS OF HISTORY. 57 

To Leopold von Ranke, who died in 1880, at tlie age of 01 
years, belongs the honor of having" transformed the Seminars 
of Germany from religious institutions into scientific labora- 
tories. In some of our universities this method is used in 
connection with others, but it is obviously impracticable in 
schools of lower grade. It is intended solely for such stu- 
dents as desire to make a specialty of history. 

53. Tlie Eclectic Metliod. — " All roads lead to Rome, " 
says the proverb; so, all methods must be known and used 
by the teacher, if he w^ould attain to the highest success in 
his profession. Better than any one method is a combina- 
tion of all methods, provided that this combination is deter- 
mined by an intelligent appreciation of the requirements of 
each particular situation. No teacher ever became great in 
his profession by pursuing undeviatingly a single plan of 
procedure. Napoleon's successes were owing, not to superior 
forces, but to superior genius in adapting means to ends; in 
bringing to bear, in a particular emergency, just the agencies 
required to accomplish his purposes. His plans and military 
processes were eclectic — determined by circumstances; the 
methods of his enemies were in accordance wath the estab- 
lished principles of military science. They could not deviate 
from the beaten track — they were hampered by the rules 
learned from their teachers. 

The conditions of success for a teacher are exactly similar. 
Means and methods must be various, suited, in each case, to 
requii'cmcnts; any single plan long pursued becomes monot- 
onous and ineffective. The Eclectic method aims at variety, 
freshness, and the sustainment of interest. It is a method 
made up of elements selected from all sources, and deter- 
mined by existing circumstances. More than any other, it 
requires in the teacher judgment, and an exact imderstanding 
of his pupils and of the subject that he is teaching. Properly 
u.sed, it is the best of all methods, for it takes into account, 
in each case, the needed elements of success, and .these are 
always unique — always peculiar. At one time, he lectures; 
at another, he questi(jns; now he tells a story in illustration 



58 PEDAGOGlCvS OF HLSTORY. § G 

of some point; again, he resorts to researeh by the pupil; 
sometimes a historical poem or ballad is read; sometimes the 
pupil prepares a thesis. Here is a lesson furnishing instruc- 
tion in ethics — in moral beauty; here, one dealing with 
political economy and good citizenship. No opportunity of 
utilizing side issues is lost, but thoughtfully, wisely, discrimi- 
natingly, the teacher employs every means of imiting the 
multitude of lessons and principles and inferences into a 
coherent, symmetrical, logical whole. 

53. Conditions of Success. — But this is a method 
requiring in the teacher rare powers of management and 
of organization, as well as comprehensive and thorough 
acquaintance with his subject. It is, moreover, a method 
that induces rapid growth, not only in the pupil, but in the 
teacher himself. Each year reveals some imperfection in 
the devices and processes of the last year's work. It is, in 
short, a method of growth, of evolution, and in its best 
phase it is the climax and perfection of all methods. Its 
employment induces and develops in the teacher that best 
of all attributes, originality; and the example to the pupil 
of an intelligent use of appropriate means will become an 
influence in all his after life. 

One special error of procedure is likely to attend the use 
of the Eclectic method; indeed, it is to be guarded against 
with every method. It is the probability of obscuring the 
general plan by side issues. Always, when the logical con- 
nection is broken by an illustrative aside, by an applicati(Mi 
of some principle to a particular case, or by an ethical or 
economic deduction, the main thread should be formally 
and distinctly resumed. At such points, it is well for the 
teacher to require from the pupils a resume of the chapter or 
lesson up to the point where the break occurred, for it must 
not be forgotten that a coherent logical whole is the matter 
important above all others. Everything else should be made 
secondary to this, and when a historical work is finished, it 
should lie in the mind of the class with all the definiteness 
of a landscape. In the consideration of fact or application, 



§ G PEDAGOGICS OF HISTORY. 50 

of illustration or inference, do no^t lose sight of the g-eneral 
scheme. 

54. Observations Upon Methods. — Whatever method 
or combination of methods may be employed by the teacher 
of history, little will be accomplished unless the pupil gives 
his best powers to the study. The teacher's contribution to 
the work is, in the nature of things, only directive. He may 
superintend the work wisely and with comprehensive views, 
or he may not; but the final outcome depends largely upon 
what the student does for himself. There is a growing 
notion that if we can but have a good teacher, his work will 
so supplement what the child may do, whether that be well 
done or otherwise, that the result will be satisfactory The 
goodness of a teacher, however, is in large measure deter- 
mined by what he can induce the pupil to do for himself. 
Before comparisons or applications can be made, or laws 
inferred, there must be a basis of facts in the mind of the 
pupil; and with this working material he must be perfectly 
familiar. This is to be acquired by the pupil's own efforts. 
In this, the teacher's aid avails but little. To be a scholar 
in any proper sense, one must " biirn the midnight oil." 
And, contrary to an opinion entertained by some and too 
much encouraged by medical incompetents, this mental work 
expended in study and acquirement is undoubtedly good for 
the mind, and is not hurtful to the bodily powers; for, it is 
a well known fact that when business men, after having been 
actively engaged for years in the most intense activity of 
body and mind, retire for "rest," the repose of the grave 
quickly follows. 

This use of the memory in accumulating the facts of his- 
tory is especially important and necessary in the earliest 
school work. Dr. W. T. Harris, Commissioner of Educa- 
tion, says: 

"The elementary school will always have the character of memory 
work stamped upon it, no matter how much the educational reformers 
may improve its methods. It is not easy to overvalue the work of such 
men as Pestalozzi and Froebel. But the child's mind cannot seize great 



HO PEDAGOGICS OF HIvSTORY. §(5 

syntheses. He bites off, as it were, only small fragments of truth at 
best. He gets isolated data, and sees only feebly the vast network of 
interrelation in the world. This fragmentar}^ isolated character 
belongs essentially to primary education." 

Referring to the importance of a disciplined and retentive 
memory, Professor Hinsdale quotes the following from the 
" Psychology " of Professor James: 

"No one, pi-obably, was ever effective on a voluminous scale with- 
out a high degree of this physiological retentiveness. In the practical 
as in the theoretic life, the man whose acquisitions stick is the man 
who is always achieving and advancing; while his neighbors, spending 
most of their time in relearning what they once knew but have for- 
gotten, simply hold their own. A Charlemagne, a Luther, a Leibnitz, 
a Walter Scott — any example, in short, of your quarto or folio editions 
of mankind, must needs have amazing retentiveness of the purely 
physiological sort. Men without this retentiveness may excel in the 
quality of their work at this point or that, but they will never do such 
mighty sums of it, or be influential contemjioraneously on such a 
scale." 

55, Suiiiniary. — -The Memoriter method, therefore, so 
far, at least, as acquirement is concerned, is one of extreme 
importance in the early stages of history study. The prin- 
cipal thing to be guarded against, as has already been 
explained, is the memorizing of lessons in the exact words 
of the author. The means of guarding against this have 
already been mentioned and emphasized. The thought 
expressed is the principal thing, and, in arriving at the 
thought with exactness and precision, there should not 
remain in the text one word whose meaning, as there used, 
is in the slightest degree vague. This is largely a work to 
be looked after by the teacher. The habit of resting con- 
tent with nothing that is indefinite or uncertain, of follow- 
ing everything to its last analysis, is not easily formed, and 
the teacher that establishes and confirms such a mental 
habit in his pupils has done much for their later educational 
growth. In the formation of such a habit, it must be 
remembered that the relation between words and the 
thoughts they are intended to express is very uncertain — 
scarcely anything is more so. There are very few writers 



§ 6 PEDAGOGICS OF HISTORY. 61 

that so choose their words as to say exactly what they mean, 
and it is from the context and from our own knowledge of 
the subject, that exact meanings must often be gathered. 
It is, therefore, a part of the teacher's work to clear away 
ambiguities that come from the careless and indiscrimina- 
ting use of words. The same may be said of arrangement. 
The teacher will often be required to adjust parts that are 
out of proper logical or chronological relation. 



RELATIOI^ OF HISTORY TO OTHER 
SUBJECTS. 



PIIKI^IMINAIIY CONSI]>EUATl()XS. 

5(5. V^astuess of tlie Subject of History. — In the early 
years of the present century, it was- possible for a student to 
become tolerably familiar with almost the entire field of 
ordinary human learning, at least so far as it had been 
written in our own language. Comparatively little had been 
done in the physical sciences and in mathematics. Most of 
the scholarship of the world was engaged in endless disputes 
about metaphysics, theology, and other nebulous subjects. 
It is true that some great historical work had been done, but 
in all of it, the real, the inner life of the people, was almost 
completely ignored. Historical investigations were not 
minute and scientific, as they are now. Kings and courts, 
and political intrigues, and battles, and military leaders 
absorbed the attention of historians, to the exclusion of what 
is now regarded as history. Modern methods of investiga- 
tion have since been introduced in every quarter, and the 
domain of all the inductive sciences has been expanded to 
such an extent that no person can hope to master completely, 
in our short lifetime, any one subject, even if he neglects 
every other. 

In a recent conversation with, perhaps, one of the greatest 
of living organic chemists, he said to the writer that a perfect 



(i2 PEDAGOGICS OP^ HISTORY. g i; 

knowledge of organic chemistry would involve the necessity 
of remembering at least eight million formulas, processes, 
combining proportions, affinities, reactions, incompatibles, 
etc. Discussing the adjustments necessitated in educational 
methods by the division of labor in scientific investigations, 
and by the development of specialties, he said that education 
in the early future will be measured by facility in consulting 
and understanding books of reference. -However this may 
be, it is certain that the men that make their mark most 
indelibly on the scroll of the world's progress — the men 
whose success in life is the greatest for themselves and the 
most valuable to the world — are the specialists. These are 
the men that learn to do some particular thing better than 
any one else can do it. Such men compel those that seek 
the best of its kind to come to them. They are not obliged 
to seek a market for their products. Alvan Clark might 
have removed to the other side of the earth, but orders for 
the largest and best lenses that are made would have fol- 
lowed him, and he coiild have fixed his own price. Steven- 
son took refuge in far Samoa, but he could not get away 
from the demand for finished and masterly literary work. 
With respect to such men as Dickens, Gladstone, Pasteur, 
Tyndall, Bell, Tesla, Edison, the important thing is that 
they be alive. Where they may happen to be is of slight 
importance. The world will find them with its cry for help. 
This necessity for devoting one's best powers to some 
specialty is applicable also to the subject of history. He 
that wishes to become great in understanding, writing, or 
teaching history must make it a life work. He must, more- 
over, love his work. And, even if one does not mean to 
devote his attention to history exclusively, he must, to teach 
it w^ell, be a persistent student of the subject. 

57. Division of Liabor In Teaeliing;. — The assignment 
to different persons of the several parts of a task consisting 
of many elements and processes is not confined to science, 
commerce, and the various industries. Our best schools are 
doing the same thing. And this is true not only of our 



§ 6 PEDAGOGICS OF HISTORY. 63 

colleges with their professors for special subjects, but also 
of many of our public schools. The best teacher of mathe- 
matics teaches mathematics, and the same arrangement is 
made with respect to other subjects. And this is a usage 
that is growing and has come to stay. It is reaching farther 
and farther down along the grades in our system of educa- 
tion. When our population becomes denser the graded 
system will be introduced even into our country schools, and 
we shall have different teachers in language, in reading, in 
writing, in geography, and in history. Even the little folks 
of the kindergarten will look to one teacher for their knowl- 
edge of numbers, to another for manual devices and physical 
expertness, and to still another for language training. No 
machinist can make equally well the various parts of a loco- 
motive ; neither can a teacher secure equally good results in 
every school study. 

The extension of the division of labor to teaching is .some- 
thing to be wished for and encouraged. Many of our cities 
and towns have introduced it, and, wherever this has been 
done, its great advantage has been demonstrated. Should 
the introduction of the division of labor in the work of 
education become general, it will necessitate the training 
of teachers in special subjects; and, although a generous 
all-sidedness of culture in a teacher will still be required, 
the one subject for which he has the greatest liking and 
aptitude will be emphasized in his preparatory training. 

58. Objections to Sijecializatioii in Mental and 
Physical Training. — Nowhere in the world has devotion 
to single subjects of study been more general than in Ger- 
many. Critics of German culture have made the point that 
such special training in one subject has the effect of dwarfing 
in every other. They allege that the Germans do not have 
a single complete history of their own country — only an 
unorganized collection of brilliant treatises, each of which 
covers a particular period. This is doubtless true, but is it 
something to be deprecated ? It may be said, in answer, 
that if one desires the best possible treatment of almost 



64 PEDAGOGICvS OF HISTORY. § 6 

any subject, he must go for it to the Germans. The best 
cyclopedias, the most accurate maps, the most profound 
mathematical investigations, the ablest works on logic and 
metaphysics, the highest Greek and Latin scholarship, even 
the most excellent English grammar, and the most appre- 
ciative and scholarly edition of Shakespeare — all these are 
German. And after all is said, is it not perfection in details 
rather than imperfect general schemes that the world most 
needs ? If a great bridge is to be built, do we not seek out 
the greatest engineer available ? He does not, perhaps, know 
Greek or Sanskrit, he is not an athlete or a chemist, he is 
unacquainted with whist, and golf, and baseball ; but what 
of that ? He is great as an engineer, and that is the impor- 
tant matter. The great military leader cannot be at the 
same time equally great as the leader of an orchestra; 
Newton cannot do the work of Mozart, nor can Michael 
Angelo conduct the investigations of Faraday, Darwin; or 
Pasteur. "Jack of all trades, but master of none " is a more 
serious criticism than that urged against the specialization 
of the Germans. The world will see no more masters of uni- 
versal learning — no more Scaligers or Admirable Crichtons. 
It needs rather men eminent in specialties. Moreover, the 
most effective training is in the direction of inherited tend- 
ency. It was vastly easier to make of Patti a great singer 
and of Rosa Bonheur a great painter, than it would have 
been to make of the former even an ordinary painter and of 
the latter a mediocre singer. Find out what your boy was 
born for, and help him to become eminent if he can. Ger- 
man specialization is the only development that is perfectly 
rational and perfectly natural. 



COPtIl>:T^ATIO:N^S OF HISTORY. 

59. Interrelation of Subjects of Study. — While, 
from the foregoing considerations, it is clear that the great- 
est eminence and usefulness are attainable only by devotion 
to one subject, it is equally clear that no subject is entirely 



§ 6 PEDAGOGICS OF HISTORY. Go 

isolated from every other. Perfection in one thing implies a 
certain degree of acquaintance with many related matters. 
The great scnlptor must know anatomy, human and com- 
parative; the eminent engineer must be acquainted with 
graphics, the strength of materials, the laws of momentum, 
the effects produced by changes of temperature, and the 
general properties of matter. Similarly, the subject of his- 
tory has its related subjects. These are many, and each is 
extensive enough to constitute a life work for the greatest 
intellect. The student or teacher of history, therefore, can- 
not know all these thoroughly. The field is too wide for the 
brief span of life. He may, however, understand their gen- 
eral principles and the nature of their connection with his 
specialty. Before entering upon a consideration of the sub- 
jects with which history is correlated, it is necessary to 
understand the meaning of correlation as used in educational 
science. 

60, Meaiiini>' of the Term ''' Correlation/'' — Tlie 
word correlation has only very recently been introduced into 
pedagogical writings. The consequence is that its precise 
signification, when so used, has not yet been settled. The 
term, as generally used, may be defined as the act of bring- 
ing into mutual or reciprocal connection, action, or corre- 
spondence, two or more persons or things, or it is the state 
of their being in such relation. Applied to the subject mat- 
ter of education, there is much diversity of meaning attached 
to the term. By some it is interpreted to mean that all 
subjects of study are more or less closely related to one 
another; so that an adequate knowledge of any one implies 
and necessitates an equal or a partial knowledge of every 
other. To illustrate, no one can be fully acquainted with the 
subject of music, if he is ignorant of acoustics and of the 
mathematical relations of the different wave lengths in the 
propagation of sound through air; for upon these is depend- 
ent the entire theory of harmony and discord. 

01. Coiiniiittee of Fiftooii. — Others, again, insist that, 
because such relations exist among subjects of study, none 



6G PEDAGOGICvS OF HISTORY. § (i 

of them should be taught apart from the rest, but all should 
be taught in conjunction. The extreme advocates of this 
view insist that some literary work should be taken as a sort 
of text from which the study of all school subjects should 
proceed with equal step. In the report of the Committee of 
Fifteen, and in the discussion that followed, reference is 
made to the story of Robinson Crusoe as such a center, from 
which every needful study may be evolved and fully taught. 
The following quotations from the report of that committee 
will be instructive : 

" Your committee would mention another sense in which the expres- 
sion ' correlation of studies' is sometimes used. It is lield by advocates 
of an artificial center of the course of study. They use, for example, 
Defoe's 'Robinson Crusoe' for a reading exercise, and connect with it 
the lessons in geography and arithmetic. It had been pointed out by 
critics of this nietliod that there is always danger of covering up the 
literary features of the reading matter under accessories of mathematics 
and natural science. If the material for other branches is to be sought 
for in connection with the literary exercise, it will distract the attention 
from the poetic unity. On the other hand, arithmetic and geography 
cannot be unfolded freely and comprehensively if they are to wait for 
the opportunities afforded in a poem or a novel, for their development. 
A correlation of this kind * * * * is a shallow and uninteresting kind 
of correlation, that reminds one of the system of mnemonics, or artificial 
memory, which neglects the association of facts and events with their 
causes and the history of their evolution, and looks for unessential 
quips, puns, or accidental suggestions with a view to strengthening the 
memory. The effect of this is to weaken the power of systematic think- 
ing which deals with essential relations, and to substitute for it a 
chaotic memory that ties things together through false and seeming 
relations, not of the things and events, but of the words that denote 
them. 

"The correlation of geography, and arithmetic, and history, in and 
through the unity of a work of fiction, is at best an artificial correlation, 
which will stand in the way of the true objective relation. It is a 
temporary scaffolding made for school purposes." 

Farther on the report contains the following: 

" The story of Robinson Crusoe has intense interest to the child as a 
lesson in sociology, showing him the helplessness of isolated man and 
the reenforcement that comes to him through society. It shows the 
importance of the division of labor. ****** Consequently, the 



§ 6 PEDAGOCxICS OF HISTORY. G7 

history of Robinson Crusoe is not a proper center for a \'ear's study in 
school. It omits cities, governments, the world commerce, the inter- 
national jDrocess, the church, the newspaper and book from view, and 
they are not even reflected in it." 

6'^. Remarks Upon the Foregoing- Quotations. — 

The writer believes that the abstirdity and uselessness of the 
method of correlation described and criticized in the fore- 
going quotations will be sufficiently obvious to every 
thoughtful teacher. It appears to be necessary, however, 
that some additional comments should be submitted. 

In the first place, then, there seems to be little question 
that every subject of study should be taught as a distinct 
entity — as isolated and complete in itself — except in so far as 
matters belonging to other subjects are used to illustrate and 
emphasize its principles. These illustrations should, in 
general, bear a relation to the main subject similar to that 
in geometry between a demonstrated proposition and a 
corollary to it. These correlation extremists have a notion 
that many branches can be successfully studied together, 
and that the law of association is thus utilized in the best 
possible manner. As well might one attempt to learn a half 
dozen trades at the same time. It is not meant that, when 
we study one subject, its relations to others must be care- 
fully excluded from consideration; it is intended only that 
side issues must not be permitted to cloud, and so to divert 
attention from the main subject as to destroy its unity. 

And just here the writer may be permitted to remark that 
teachers especially should endeavor to see matters in proper 
proportion and with due reference to their relative impor- 
tance. The world is full of enthusiasts on every subject, of 
people that have discovered the "much sought kaloii." 
These people imagine that they can tell us how to do per- 
fectly what the world has hitherto been able to do only 
indifferently well. They know an infallible remedy for 
every disease, and how to perfect every process or method. 
To them, everything that is, is cankered, and the world has 
been waiting and yearning for their arrival to set things 
right. There is something contagious about the enthusiasm 



68 PEDAGOGICvS OF HISTORY. § 6 

of these evangelists of "fads," and teachers should not 
permit themselves to be deluded by trivial matters that have 
been exaggerated out of all proportion to other things. The 
teacher of music comes to imagine that, in our schools, his 
speciality is the main thing — that children are created prin- 
cipally in order that they may sing. Everything else should 
be subordinated to music. The man employed to super- 
vise drawing, the teacher of physical training, of sewing, 
of cooking, of manual training, the instructors, in short, in 
the various other "educational fringes, " as some one calls 
them, all labor under a similar hallucination. Their zeal in 
urging the claims of their several specialties has resulted in 
crowding into the curriculum of the schools many matters of 
slight educational value, to the neglect or exclusion of others 
that are really essential. They smile in a commiserating 
way when any teacher or educator ventures to protest. 
"Poor fellow, he is behind the times; he forgets that the 
world is progressing in educational science, even though he 
himself makes no advance. " He has to bear the odium of 
being regarded as an apostle of the " three R's. " The fact is 
« that all these matters have educational value, but relatively to 
many others, their value is very slight, and not overshadow- 
ing, as their advocates actually believe. These subjects are 
like the quantities known in mathematics as iiifiiiitesiinals, 
which denote real quantity indeed, but which, in comparison 
with finite quantity, may be regarded as zero and dropped 
out of consideration. 

But this tendency to exaggerate the importance of the 
subject that one knows best, and can teach best, is general. 
The teacher that can teach languages best imagines that his 
specialty is of paramount value, and so on for the others. 
It would be difficult to overstate the importance of the 
teacher's having definite and correct views of comparative 
educational values. Having such views, he will know what 
amount of time and effort should be given to each branch, 
and he will preserve a wise conservatism with respect to the 
new matters that are constantly being urged for a place in 
the course of study. 



g (> PEI)A(i()(;iCvS OF HISTORY. (iO 

G3. Correlation of History Witli (ieog'rapliy. — As 

has been stated, it is not meant that correlated subjects are 
to be taught together and finished at the same time. It is 
intended only that certain facts belonging to one subject have 
an illustrative bearing upon another, and serve to emphasize 
it, and give broader and more significant views concerning it. 
These facts aid in discovering general laws. This is espe- 
cially the case with physical and political geography as aids 
in the study of history. The settlement of countries, the 
development of colonies, the direction and rapidity of this 
development, the rise and fall of civilizations, the products 
of the earth and their exchange among nations; all these, 
and many other factors affecting the history of the world, 
are not fortuitous — the result of mere chance. They are 
determined more by the physical features of the earth than 
by any other influences. River basins, mountain systems 
affecting rainfall and climate, ocean currents and their 
accompanying air currents, elevations of surface, and innu- 
merable other facts of physical geography have dominated 
the history of the world to such an extent that they must be 
taken into account in any intelligible view of the progress of 
the race. All these must be noted in teaching history. For 
example, in the history of America, why are the great com- 
mercial centers just where they are ? What gives Chicago, 
Philadelphia, Duluth, Mobile, New Orleans, Charleston.^ San 
Francisco, New York, and Boston their importance ? Upon 
what do the fertility and climate of the Pacific States depend, 
and why are the states between the Rocky Mountains and 
the vSicrra Nevada nearly rainless ? Upon what does their 
prosperity largely depend ? To what are owing the wealth 
and fertility of the Mississippi Valley and the Atlantic 
Slope ? Why were the original thirteen colonies all included 
between the ocean and the Appalachian System ? What 
influence are railroads, and artificial waterways, and irriga- 
tion likely to have upon United States history ? What 
advantages do we derive from our geographical isolation, 
and what are the chief arguments in favor of and against 
a policy of colonization ? Such are some of. the questions 



:(i PEDAGOGICvS OF HISTORY. § 

having' a bearing upon the study of history. Political geog'- 
raphy, too, throws a flood of light upon history. The 
thoughtful teacher, with these side lights, can give unity, 
coherence, and interest to history to an extent that is possible 
in no other way. With their aid, laws and principles emerge 
from confusion and detail, and events take on a new and 
deep significance. ' History ceases to be a mass of unrelated 
facts and dates, and its determination by the laws of cause 
and effect — of necessaiy sequence not in time merely, but 
in every other important relation — becomes apparent. 

(54. Correliition of History VYitli Sociology and 
Political Science. — The term sociology, as the name of a 
science, is intended to include in its scope "the origin and 
history of human society and social phenomena, the progress 
of civilization, and the laws controlling human intercourse." 
Sociology is not to be regarded as mere history, but as a 
philosophical study of society. But considerations relating 
to men as forming society are so closely allied to those 
relating to men as organized politically and forming states, 
that the teacher of history is not properly ecjuipped for his 
work unless he is familiar with the data, the inductions, and 
the generalizations of sociology. The remarkable work of 
"Sociology," by Herbert vSpencer, is indispensable to the 
teacher of history. It will bear reading many times. If, 
besides, the teacher has access to the same writer's monu- 
mental work on "Descriptive Sociology," the source from 
which Mr. vSpenccr largely gathered the material for his 
" vSociology, " great advantage will be derived. 

Equally close in correlation with history is political 
economy, or "that branch of civics that treats of the nature 
of wealth and the laws of its production and distribution, 
including all the causes of prosperity and the reverse. It 
discusses labor, wages, population, capital, money, rent, 
value, trade, and the relation of government to industry and 
economic conditions." With a knowledge of the principles 
and laws of political economy, which are themselves derived 
from human experience as revealed by history, the teacher 



§ G PEDAGOGICS OF HISTORY. 71 

can interpret for himself the canses and consequences of 
political action, and make them clear to his pupils. The 
principles that regulate good and bad political action, both 
in individuals and in nations, are but dimly seen without the 
guidance of political economy. Many excellent treatises on 
this subject are of easy access, but perhaps one of the best 
is Professor Laughlin's abridgment, with notes, of the work 
by John Stuart Mill. 

Under the general science of civics is included the subject 
of international law and usage. This, with reference to ques- 
tions arising in war, is, at this writing, of especial interest 
in the United States. Every teacher should be familiar 
with this subject, particularly if he is a teacher of history. 
President Woolsey's work, and that by George B. Davis, 
Judge Advocate of the United vStates Army, will be found 
interesting and instructive. 

G5. Correlation of History Witli l^tliios. — Ethics, or 
"the science of human conduct considered with respect to 
rightness and wrongness, " includes, in its most general 
sense, the various branches of political and social science, 
civil, political, and international law and jurisprudence. In 
its application to history, it is intended to consider the moral 
quality of individual and national conduct which, next to 
cause and effect, is one of the most instructive aids in the 
teaching of history. Without it, action is divested of that 
which makes it distinctly human, nations and individuals act 
without conscience, and history engages only the intellect. 
" Was it right or was it "wrong ? " "What should he have 
done under the circumstances ? " "Was the punishment in 
this case deserved ? " " Did the nation act in this instance 
as an individual should have acted ? " These, and innumer- 
able c[uestions like them, should constantly be started with 
thoughtful pupils. Judiciously employed, they serve rather 
to emphasize than to destroy the unity of history. The 
teacher, therefore, should be acquainted with both theoret- 
ical and practical ethics, and should be skilful in applying 
their principles to the subject he teaches. Of the sources of 



n PEDACiOGlCS OF HISTORY. § (1 

information, no special mention need be made, for there are 
innumerable treatises readily available. 

6G. Conclusion. — It is hoped and believed that what 
the writer has herein set forth with much care, and which 
he has gleaned from many years of personal experience in 
the classroom, from many other years in supervising the 
work done by others, and from inuch reading both of writers 
of our own land and of France and Germany, will prove to 
be valuable to the student and spur him to higher ambition 
to excel. However this may be, one thing is certain; he 
that would succeed in the difficult and useful profession of 
teaching must himself earn success. . He should form a 
habit of self-criticism, and aim to do, year after year, better 
work than ever before. He should not be willing to settle 
down into routine methods, always doing the same things in 
the same way. Some one has said that poets and teachers 
are inade in heaven. Such aphorisms may, many of them, 
be relegated to the limbo of fancy. wShall we not rather say 
with Richelieu ? — 

" In the lexicon of j-outh. which 
Fate reserves for a bright manliood, there is no such word 
As—/ai/." 



PEDAGOGICS OF ORTHOGRAPHY. 



IXTRODirCTIOX. 



DEri:N^iTio:N^s and ci^assifications. 

1 . Defliiitiou of Orthogi'Jiphy. — The word ortliograpJiy 
is derived from the Greek dfr^ix;, ortlios, right, and ypdcf)Fiv, 
graplicin, to write. Its literal meaning is, therefore, ivri- 
ting correctly. As commonly used, it means "a mode or 
system of spelling-, especially of spelling correctly or accord- 
ing to nsag-e." In a usual and wider sense, orthography is 
the science or art that treats of letters and .spelling, inclu- 
ding orthoepy, or correct pronunciation, and phonology, or 
pJioiietics, which is the science of "human vocal sounds, 
their relations one to another, and their interchanges." 
Orthography was, until recently, classified as one of the four 
divisions of grammar, the other three being etymology, 
syntax, and prosody. It is properly a branch of grammar, 
but its treatment has been relegated to the spelling- book 
and the dictionary, just as the subject of pro.sody has been 
turned over to the works on rhetoric. But the complete 
separation of orthography from grainmar is not possible, 
and, perhaps, not desirable. If the student will examine 
any of our spelling books, he will find that the derivation, 
the composition, and the meaning of words have in these 
books much to do with the arrangement and general treat- 
ment of orthography. But these are questions of etymology^ 



2 PEDAGOGICS OF (JRTHOGRAPHY. §7 

which has been retained as one of the two general divisions 
of grammar as now treated. In this Paper, therefore, it 
will be assumed that orthography includes every considera- 
tion with respect to words that will aid in mastering their 
spelling and pronunciation. 

3. Alpliabets. — The term alphabet is made up of alpha 
and beta, the names of the first and the second letter of the 
Greek alphabet. Of thisw^ord, Max Mliller, the great philol- 
ogist, says, "The only word that is formed of mere letters 
is alphabet, the English a-b-e." 

The invention of the earliest alphabet is lost in the time 
prior to authentic history. Authorities are mostly agreed 
that the oldest writings in which letters are combined in 
words are the Hebrew writings. The earliest letters of the 
Hebrew and the Phenician alphabet are almost identical in 
name, form, and sound, and it is impossible to say which 
alphabet is the older. It is stated in the "Encyclopaedia 
Britannica " that the Phenician alphal^at w-as the parent of 
almost every alphabet, properly so called, existing on the 
earth. Of the Greek alphabet, from which our own is in the 
main derived, Dr. Raphael Kiihnersays, " The Greeks derived 
most of their alphabet from the Phenicians. According to 
the common tradition, letters were brought into Greece by 
Cadmus, a Phenician. The Phenician alphabet, being nearly 
the same as the Hebrew, consisted of twenty-two letters. 

Nineteen letters of the Phenician alphabet were 

adopted by the Greeks as alphabetic characters. These are 
the first nineteen letters of the present Greek alphabet. To 
these the Greeks themselves added the last five letters; viz., 
npsiloii, phi, cJii, psi, and omega. This seems to be the most 
rational view of the formation of the Greek alphabet, though 
somewhat different from the common legendary account." 

The legendary account referred to above is as follows: 
Cadmus, a son of Agenor, King of Phenicia, was sent by his 
father in quest of Europa, who had been carried oif by 
Jupiter. Ordered not to return without his sister, and having 
failed to find her, Cadmus settled in Breotia. He introduced 



§ 7 PEDAGOGICvS OF ORTHOGRAPHY. 3 

among the Greeks sixteen letters from the Phenieian alpha- 
bet. To these Palamedes subsequently added four more, 
thcta, xi, phi, and chi ; and vSimonides, at a still later period, 
added four others, r.eta, eta, />si, and oiiifga. 

The alphabets of different nations differ in the number of 
their letters. According to one of our latest authorities, the 
Italian alphabet has 31 letters, Hebrew and Syriac 23, Latin 
23, Greek 2-i, French 25, English, Dutch, and German 2G, 
Spanish 27, Arabic 28, Coptic 32, Russian 33, Armenian 3S, 
Georgian 39, Slavonic 40, Persian 45, Sanskrit 49, etc. 

The Chinese language has no alphabet, but it has instead 
about 30,000 arbitrary characters. The language is said to 
be uicviosyllabic, thougli the word syllabic (from the Greek 
avv, sj'ii, together, and /iaiiiiavco, lamba)u\ I take) implies 
separable parts having vocal completeness. It is obyious, 
therefore, that a good alphabet is an extremely important 
aid to human learning, and, hence, to civilization and prog- 
ress. For example, the chief obstacle in the way of the 
advancement of the Chinese is the fact that they have no 
alphabet, and, thjrefore, practically no language that can be 
read and understood by the common people. General cul- 
ture is, therefore, impossible. To learn to understand and 
write 20,000 arbitrary characters having nothing in common, 
and without anything but local agreement to determine their 
pronunciation, is a life work even for a person above ordi- 
nary intellectual endowment. Having no letters, they have 
no established sounds, and, hence, no general code of pro- 
nunciation. It results, therefore, that, while two learned 
Chinese are able to read and understand the same book, they 
may be unable to converse with each other. Most of the 
common people in China are unable to read and write, and 
those that can do so have vocabularies limited to a few hun- 
dred words in daily use. 

In solving the problem of civilizing such a people, the first 
requisite is to devise for them an alphabet. Such an inven- 
tion would necessitate the abandonment of their language, 
and the learning of a new one. But all human experience 
in such reforms demonstrates that the total obliteration of 



4 PEDAGOGICS OF ORTHOGRAPHY. § 7 

an established language, and the substitution of another 
entirely different, is impossible. In confirmation of this 
statement, it is necessary only to mention the result of the 
many attempts to improve our own language. Such changes 
must not be radical, and mvist be wrought by the slow proc- 
esses of evolution. These considerations lead to the unavoid- 
able conclusion that the same fate awaits the Chinese that 
has overtaken the North American Indian and many other 
aboriginal races of the world. The superiority of the old 
Greek civilization was doubtless owing largely to the fact 
that their language was more nearly perfect than any other 
that has ever been devised. The "decline and fall" of 
nations, when face to face with superior civilizations, is 
owing more to differences in language structure than is 
generally supposed. It is merely a result of the operation 
of the law of "the survival of the fittest," involving the 
obliteration of the unfittest. 

For further information relative to this curious and inter- 
esting subject, the student is referred to Isaac Taylor's 
"The Alphabet." 

3. J^ames of tlie Letters and IIo^v to Write Tliem. — 

In pronouncing the names of the letters of the English 
alphabet there is general uniformity, but in writing and in 
pluralizing their names the case is otherwise. Goold Brown 
says, " The names of the letters, as now commonly spoken 
and written in English, are A, Bee, Cci\ Dcl\ E, Eff^ Gee, 
Aitch, I, Jay, Kay, Ell, Evi, En, O, Pee, Kiie, A?', Ess, Tee, 

U, Vee, Doublc-u, Ex, IVy, Zee I know not 

whether it has ever been noticed that these names, like 
those of the days of the week, are worthy of particular dis- 
tinction, for their own nature. They are words of a very 
peculiar kind, being nouns that are at once hotli proper and 

covinnvi Their names, therefore, should always 

be written with capitals, at least in the singular number; 
and should form the plural regularly. Thus, A, Aes ; Bee, 
Bees ; Cee, Cees ; Dee, Dees ; E, Ees ; Eff, Effs ; Gee, Gees ; 
A it ell, Ait c lies ; I, les ; Jay, Jays ; Kay, Kays ; Ell, Ells; 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 5 

Eui, Ems; Ell, Ens ; O, Ocs ; Pec, Pecs; Kite, Kucs ; Ar, 
Ars ; Ess, Esses; Tec, Tecs ; U, Ucs ; Vcc, Vers; Doiiblc-u, 
Doublc-ucs ; Ex, Exes; W'j, IVws ; Zee, Zees." 

Brown quotes from Shakespeare, " Then comes answer like 
an A B C book." " Then comes question like an a, b, c, book." 
Of these he remarks, " Better: ' like an A-Bee-Cee book,' " 

It will be noted that Brown distingfuishes between the 
alphabetic characters and their names. But is such a dis- 
tinction necessary ? The w^riter thinks not. Let the student 
consider the following, and decide which is better: 

" Cross your /'s and dot your /'s. " " Cross your Tees and 
dot your les. " 

' ' The word pepper is half /'s. " ' ' The w^ord pepper is half 
Pees. " 

" There are two /r's in /itr/i, and two 7i''s in ielie7i>. " " There 
are two A itches in hah, and two Doiib/e-ues in wlieivS' 

" How many j"'s and how many j''s in syllable ? " " How 
many Esses and how many Wies in syllable? " 

The same reasoning that makes A itch a proper name 
would make the name of a prefix, a suffix, a root, a word, or 
of any symbol, a proper noun; but no one thinks of writing 

any of these as proper nouns. Thus, 5, +, (^, 4/, etc., so far 



as their written names are concerned, are five, plus, clef, 
radical sign, and not Five, Plus, etc. In the plural, also, 
Brown writes the names of the letters wath capitals; now, it 
is well known that a noun strictly proper cannot take the 
plural, for it is a name peculiar to an individual. It is true 
that we have a usage like the following, in which the capi- 
tal is retained : 

" There are more Georges than Henrys in this school, and 
more Marys than Elizabeths.'' 

"The Shakespeares of the world have done more for its 
advancement than the Napoleons." 

But these words so used are class names, and hence, 
although they are written with capitals, they are common 
nouns. Besides, in pluralizing such words, we do not u.sually 
follow the general rule, but add s. Thus, Mary pluralized 



G PEDAGOGICS OF ORTHOGRAPHY. § 7 

is Marys, not Maries, and Henry is Henrys, not Henries. 
But Brown makes JT/rj- the plural of Wy, Aes the plural of A, 
and C/es the plural of 6^^, It is extremely doubtful whether 
any considerable number of people could interpret the fol- 
lowing sentence, if the meaning of the writer were not 
indicated by the context: 

"The vocal values of the JVies are different in sysyg-y, 
which totally lacks Double-iies.'' 

But the meaning is perfectly plain when these strange 
words are written j''s and tl-'s. 

4. Symbols and Tlieir Plurals. — It should be noted 
that, with the exception of letters and Arabic numerals, it is 
generally better, especially when the plural is required, to 
write i}i words what is meant by mere symbols. Thus, we 
should prefer division signs or signs of division to -=-s or -f-'s, 

G elefs to (^s or ^'s, ratios to :s or :'s, radical sig//s to |/s 



or j,'"s, etc. But, in textbooks on particular subjects, sym- 
bols may first be explained, and afterwards used instead of 
words. Thus, in arithmetic, o-^-d = Jl is better than //le 
snni of five and six is equal to eleven ; in geometry. As is 
preferable to triangles; and in chemistry, Fe,fi^ is more 
satisfactory than sesqnioxide of iron. There are inany 
exceptions to this, however, and, in general, it is taste that 
must decide the questions that arise. There is no work in 
which the subject has been fully treated by a competent 
authority, but there is usually a way out of every difficulty 
of the kind. 

Very frequently a symbol and its explanations are both 
given, the symbol being generally enclosed in a parenthesis. 

"The sign of equality (=) denotes that the quantities 
between which it is written are equal. " 

" In works on astronomy, the planet Neptune is denoted 
by a representation of a trident {^), and the planet Venus 
by the figure of a mirror ( 9 ). " 

5. A Perfect Alphabet. — Frequent attempts have been 
made to modify our alphabet, and the dream of many that 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 7 

have realized its imperfections has been, if not to devise one 
that is perfect, at least to approacli this ideal as nearly as 
circumstances will permit. For the difficulties in the way 
are many, and some of them are insurmountable. It will, 
therefore, be interesting- to inquire what should be the leading- 
characteristics of a perfect alphabet. 

TJie spelling of a x^'ord must denote its proniineiation i^nth 
mathematical exactness. There is no language in the world 
that is pronounced precisely as it is spelled. Certainly the 
English is not. It is scarcely necessary to cite illustrations 
of this fact. The bewildering series of words containing 
ongh would suffice. A part of this series includes cough., 
plough, tough, hough, bough, sough, dough, lough, and this fact 
may explain why some one has proposed poughteigJiteaux as 
a "reform spelling" inv potatoes. 

The German is often mentioned as a language in which the 
spelling of words indicates their pronunciation, but this is 
only partially the case. For example,^-,'", d, and.?, when final 
in words and syllables, are not pronounced as when they are 
in other positions, and these differences are not uniform 
throughout Germany. Thus, s in Ihsinarck is sounded like 
s in sir, and .S" in Sohn is like our z ; g in Ding\^ very nearly 
our /', and in guter, g is like g in good ; etc. Many other 
variations in the sounds of particular letters might be noted, 
but it is not necessar3\ 

There must be as many different characters as there are 
elementary sounds. This condition is not realized in the case 
of any language, and in the nature of things cannot be, for 
no instance can be found of uniformity of pronunciation in 
different parts of any given coimtry. In the United States, 
for example, the authorized sound of a in glass, mass, pass, 
etc. is very commonly displaced by the short sound of a as 
heard in mat ; and a short (a) in barrel, marry, etc. are gen- 
erally pronounced as a in arm. One of our latest and best 
dictionaries recognizes this divided iisage by an article on 
"Variant Pronunciation," in the course of which we find, 
"A few of the most common cc^iditions of variation have 
been applied, the most important of which are in 



8 PEDAGOGICS OF ORTHOGRAPHY. § 7 

words colloquial and words technical or scientific. Others 
occasionally introduced are poetical, devout, hmnorous, in 
certain old phrases. Pronunciation is really a work of art, 
one of the fine arts. A great orator or [a] conversationalist 
deals with varying shades of voice as an artist with the tones 
of a violin. " 

Richard Grant White, in "Words and Their Uses," says, 
" In pronunciation, the usage of the most cultivated people 
of EnglivSh blood and speech is absolute, as fa?' as their 7isagc 
itsc/f is fixed. Pronunciation is the most arbitrary, varying, 
and evanescent trait of language; and it is so exceedingly 
dilificult to express sound by written characters that to con- 
vey it upon paper with certainty, in one neighborhood for 
ten years, and to the world at large for one year, is practi- 
cally impossible. " 

Every eoinbiuatioii of sounds in 7uords must eoalesee easily. 
If the student will pronounce a few words like /ist/essness, 
/>artie7(/ar/y, and stre)igtJie)iedst, and will note the degrees of 
difficulty in adjusting the tongue, teeth, lips, palate, throat, 
etc. as he passes from syllable to syllable, and if afterward 
he will do the same with such words as lullaby., Agameniuou, 
tintinnabulation., and harmonious., he will understand what 
constitutes easy and difficult coalescence. Upon easy coales- 
cence depends not only the music of words, but also the har- 
mony of language. A perfect alphabet must contain no 
gutturals and hissing sounds, and no broad vowels like the 
German a ; and a musical language must abound in liquids 
and labials — /, ;//, ;/, r, /, b. 

Some one says, "If Zeus were to visit the earth he would 
speak only the Greek of Plato," and yet Plato's Greek con- 
tains one of the most ofifensive of gutturals, % sounded as cJi 
in loeJi, and has several hissing sounds. The Greek has by 
no means a perfect alphabet. The student is doubtless 
familiar with the following: "I would speak Spanish with 
the gods, Italian with my lady friends, French with my gen- 
tlemen friends, German with soldiers, Hungarian wnth horses, 
English with geese, and Norwegian with — His Satanic 
Majesty." 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 9 

(y. Spelling- Reform. — An eminent writer on grammar 
says, " Had we a perfect alphabet, containing one symbol, 
and only one, for each elementary soimd; and a perfect 
method of spelling, freed from silent letters, and precisely 
adjusted to the most correct pronunciation of words; the 
process of learning to read would doubtless be greatly facili- 
tated. And yet, any attempt toward such a reformation, any 
change short of the introduction of some entirely new mode 
of writing, would be both unwise and impracticable. It 
would involve our laws and literature in utter confusion, 
because pronunciation is the least permanent part of lan- 
guage; and, if the orthography of words were conformed 
entirely to this standard, their origin and meaning would, in 
many instances, soon be lost. We must therefore content 
ourselves to learn languages as they are, and to make the 
best use we can of our present imperfect system of alphabetic 
characters ; and we may be the better satisfied to do this, 
because the deficiencies and redundances of this alphabet 
are not yet so well ascertained as to make it certain what a 
perfect one would be." 

Notwithstanding the well known opposition to sudden, 
arbitrary, and radical change in anything long established, 
the attempt has many times been made to reform our alpha- 
betic characters and our spelling. These attempts have imi- 
formly failed; and this has not been due to the fact that the 
schemes proposed were less perfect than the method in use, 
but to the difficulties involved in reforming so important a 
matter as a language that is read and spoken in every part 
of the world. No one denies that the English language is 
faulty — very faulty indeed ; but, as has already been remarked, 
changes of this kind must be made slowly and gradually, and 
conformably with the methods of evolution. They must be 
efiiected by forces acting within rather than by modifying 
rules imposed from without. 

Such efforts to improve our English tongue by the influence 
of high authority and the decisions of learned bodies have 
never been abandoned. Books with many new characters 
have been printed, and introduced to a limited extent into 



10 PEDAGOGICS OF ORTHOGRAPHY. § 7 

our schools, but none of these well meant schemes has suc- 
ceeded in gaining a permanent foothold. One of the most 
notable of these attempts took definite shape in 1875 under 
the auspices and direction of the American Philological Asso- 
ciation. Professor William D. Whitney was the chairman of 
a committee whose duty w^as to determine and report a method 
of improving "the monstrous spelling of the English lan- 
guage." This committee has been continued from year to 
year ever since. After much discussion and adverse criti- 
cism, a change in the spelling of about 3,500 words has been 
recommended with all the weight of the organization men- 
tioned above, and approved by other similar associations in 
the United States and in England. The recommendations 
have scarcely been heeded or even heard of by the general 
public, although some of our latest dictionaries have endeav- 
ored to give them currency. The "Standard Dictionary" 
is the most conspicuous of these. It gives such spelling as 
foiuUd, fo)ictii\ sulfur, abnv, bafl, ciiiif, etc., and for their 
definitions refers the student to the words as commonly 
spelled. It is careful, moreover, to put "Phil. Soc." in 
capitals after each new form. 

The reception by the public of the proposed reform has 
demonstrated its futility. He would be a brave author or 
newspaper writer that would imperil his popularity by a 
book illustrating the reformed spelling. It would be inter- 
esting to know how "Pickwick Papers" would have been 
received, if its first edition had been revised before publica- 
tion by the "Pun.. Soc"; and the average reader would be 
shocked to see an edition of his favorite author after its 
' ' monstrous " spelling had been ' ' reformed. " These attemi)ts 
serve no purpose cpiite so well as they do to illustrate the 
impotence of efforts to overcome by authority the inertia of 
established usage. 

It may be said, however, that, while proposed reforms, 
even when they are much needed and perfectly reasonable 
and moderate, are imiformly ignored, they establish in some 
measure a direction for the general drift towards a better 
state of thing-s. For people in national masses refuse to 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 11 

advance in accordance with arbitrary enactments — they will 
r\.o\.folloxo or be steered^ they insist upon drifting. 

"7. other Obstacles to a Perfect Alphabet. — Before 
it is possible for i:s to secure a perfect English alphabet, 
there are many dilBculties to be overcome besides those 
indicated above. One of the g'reatest of these is to secure a 
general agreement as to the exact number and character of 
the sounds in the language. This difficulty is simply insur- 
mountable. Take for example the much disputed question 
whether initial iv and y are to be regarded as vowels or as 
consonants. If they are consonants, we should have for each 
a separate alphabetic character; if, as is urged with much 
show of truth, initial w and y are equivalent respectively 
to ^"^ and r, each. somewhat shortened, characters for these 
initials must be identical with those for their equivalents. 
To illustrate, let us suppose that w represents the sound 
of do., and y the sound of c\ then 7iv7, boot., yoke, and dap 
should be written civ/, bivt., yok, and dyp. 

Again, in order to establish a perfect alphabet it would be 
absolutely required that variant sounds be eliminated from 
our lang"uage. But this is manifestly impossible. Even 
among cultivated people there are widely different degrees 
of attention paid to the pronunciation of vowels and to the 
articulations {articiilus, a joint, as at the elbow) of syllables. 
Thus, if two words, as sufficiently attentive, were pronounced 
in turn by twenty different persons, no two of them would 
exactly agree. Unless there were collusion, we should 
expect to hear many varieties between sflsh'-nt-Ie ten'-tv 
and suf-fisJi'-ent-le dt-teii'-tiv. This matter of prommciation 
is one that is determined by many and varying conditions — 
differences in vocal organs, degrees of rapidity in utterance, 
conflicting authorities, educational and personal surrormd- 
ings, geographical differences, changes that come with the 
lapse of time, etc. 

In short, there being no imiform prommciation of words, 
there is no tmiformity in the sounds of letters, either 
alone or in combination. Hence, a perfect alphabet, if its 



12 PEDAGOGICS OF ORTHOGRAPHY. § 7 

invention were possible, would have no other value than 
as an ideal to guide us in bettering our speech — not in 
perfecting it. 

Consider the first letter of our alphabet; how many sounds 
has it ? Nobody knows. Every number from four to seven 
has been given by different authorities, and there seems to 
be no way by which these authorities can be brought to an 
agreement. 

Briefly, then, a perfect alphabet is only a dream that can 
never be realized in actual practice. To secure absolute 
unifomiity in the utterance of the sounds and words of the 
English language would be no easier, and perhaps no more 
desirable, than that all men should be in perfect agreement 
in politics and religion. It is by the discrimination of dif- 
ferences that the world is slowly led from better to better. 
The best condition for human advancement is unity in 
diversity — the fact of "many men, many minds." Pure 
mathematics is the only science that excludes every element 
of uncertainty; its results are therefore absolute — unchan- 
ging. The dream of the bigot is to have all men agree with 
him ; that of the philosopher, to have all men observe and 
think. 

8. Syllabication. — To every person that speaks or 
writes our language, its proper division into syllables is 
important; to the teacher, it is especially so. 

The objects to be sought by syllabication are variously 
given by different authors; the confusion, indeed, in which 
this subject is involved is something almost beyond belief. 
But, when all is said, the leading object of dividing words 
into syllables is to determine, as nearly as possible, their 
correct pronunciation. In general, syllabication is useful in 
enabling a child to pronounce correctly imfamiliar words, 
and it guides the writer and the printer in dividing words at 
the end of lines. In addition to these uses, some authors 
insist that syllabication should "show the derivation or com- 
position of words. " But in the attempt to effect this addi- 
tional purpose or function is found a cause of the confusion 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 13 

that invests the subject. To divide words so as to indicate 
their pronunciation is one thing; to divide them so as to 
show their composition is quite another. And these two 
objects are generally at variance — each defeats the other. 
Thus, when we divide pJiilosopJiy^ orthograpJiy^ and polysyl- 
lable so as to show their composition, we have pliilo-sop/iy 
{(f>iXeiv, to love; aocpia, wisdom), oi'tho-graphy [opdog, right; 
ypd(peiv, to write), and poly-syl-lablc (ToAvf, many; cn'r, 
together ; XaiijSdven', to take) ; when we divide them with 
reference to their pronunciation, we have pJii-los-o-phy, 
or-thog-ra-phy, and pol-y-syl-la-hlc. By the latter method 
the composition of the first two is hidden rather than 
revealed, and in none of them does syllabication indicate 
the etymology. It is, therefore, clear that we must choose 
between a syllabication that reveals the composition of 
words and one that shows their articulations (joints) when 
we pronounce them properly. Now, it is perfectly clear 
that only the linguist or philologist is specially inter- 
ested in the etymology of words, and, in this matter, he 
needs no help from syllabication. He recognizes the root 
elements without it. Hence, we arrive at the following 
principle : 

\Vo7'ds should bi' divided into syllables ivifh reference to 
tlieir pronunciation. If, therefore, the correct pronunciation 
of a word is known, its syllabication is usually evident. 

9. Degrees of Difficulty in Syllabication. — The 

syllabication of most English words is a very simple matter. 
Thus, no one need hesitate in dividing such words as gram- 
mar, inscription, prosperity, unprepared, Indianapolis, etc. 
It is necessary for him to know only how they are pro- 
nounced. But the problem is not always so simple. This 
is shown by the fact that there are thousands of words about 
which the recognized authorities are at variance. Thus, we 
have warrant equally good for clan-gor and clang-or, for 
rup-ture and rupt-ure, na-ture and nat-ure, Jin-cr-y and 
fi-ner-y, ivri-tcr and 7orit-er, cx-ci-ta-ble and ex-cit-a-ble; 
for sec-ond-a-ry, sec-on-da-ry, and scc-ond-ar-y; etc. 



U PEDAGOGICS OF ORTHOGRAPHY. § 7 

Again, we may find in any standard dictionary many 
apparent and many real inconsistencies. For example, in 
one of the latest and most generally esteemed dictionaries 
occur par-ting and part-ridge; port-age and por-ter; i^<]iis-key 
and ivJiisk-er; passive, pas-sage, and pass-er; etc. 

In many examples like the foregoing, the variations may 
be accounted for by differences in roots, meaning, accent, or 
termination, or by the liability that one division is more 
likely than another to lead to mispronunciation. Thus, if 
the word probity be divided pro-bi-ty it will naturally have 
the o long; while prob-i-ty will just as naturally make the 
o short. Such differences, however, as mass-ive and passive, 
rapt-iire and rup-tiire, naiigJit-y and Jiangh-ty, or-gan-ise 
and or-ga-non, and others like them, are not so easy to 
explain. 

10. Exercises in Syllalncatioii. — For classroom work, 
a very excellent and necessary series of exercises may con- 
sist in the syllabication by the pupils of words in lists of 
gradually increasing difficulty. In a very short time, there 
can be developed a nice judgment and a discriminating ear 
with respect to doubtful words. It is a field in which much 
desultory work has been done, but, in the way of results, 
not much of real value has been determined. Such exer- 
cises, too, have a great influence in indiicing clean, distinct, 
and accurate articulation and enunciation. 

It may be added that, notwithstanding the practical value 
of this subject, it receives almost no attention in the work of 
our schools. In many of the affairs of life, however, it is of 
the utmost importance. The person that writes letters, the 
author of books, the compositor, the proofreader, the private 
secretary, the public speaker, the singer, and many others, 
find a knowledge of syllabication indispensable to the best 
work. We may, therefore, safely assume that very soon it 
will find a well defined place in our schools. 

If the student imagines that the proper division of words 
into syllables is a self-evident, or even an easy, matter, let 
him copy and syllabicate the following words; and then let 



PEDAGOGICvS OF ORTHOGRAPHY. 



15 



him compare his work willi one, 
dictionaries of standard authority, 



and, if possible, with two, 



obligatory 

onerous 

absurdity 

inherent 

momentary 

diversity 

diverting 

savory 

vigorous 

laborious 



scarcity 

antipodes 

modesty 

perjury 

jeopardize 

seniority 

inaugurate 

culinary 

admirable 

feminine 



habitable 

nominative 

sedentary 

mutinous 

mutual 

fragile 

fragility 

versatile 

comparable 

combatant 



educator 

luminous 

mythology 

thousand 

mischievous 

naughty 

haughty 

contractor 

refractory 

refractive 



1 1 . llules for Syllabication. — The rule, Syllabicate 
ivonh so as to indicate their correct pronunciation, requires 
that we 'shall first kitoto their correct pronunciation. But 
the dictionaries are at variance in this matter with respect to 
thousands of words. It follows, then, that, if the diction- 
aries observe the rule cited above, they must differ in divi- 
ding- those words; and the fact is that they do differ. Hence, 
the only method of reaching uniformity in pronouncing and 
dividing words is for the entire English-speaking world to 
agree upon some particular dictionary as the final authority 
from which tliere shall be no appeal. But this is manifestly 
impossible, for there are many good dictionaries, each of 
which has its following. Unanimity in the choice of a 
standard authority in language is no more to he expected 
than is unanimity in voting for a president of the United 
States. A congress of learned men might be selected, and 
the task devolved upon it of adopting a dictionary, but how 
should its decision be enforced ? Besides, there is no diction- 
ary that is consistent throughout, and, almost certainly, no 
dictionary ever will be. And, again, the dictionary that is 
right today is wrong in a very brief time, for language is 
constantly undergoing change. 

This rtile requiring us to divide words so as to show how 
they are pronounced has innumerable exceptions. Thus, no 
division of cohvicl, flaccid^ flagitious, propitious, or venison 
can indicate their pronunciation, neither can these words be 
rightly pronotmced so as to gttide in their S}'llabication. 



16 PEDAGOGICS OF ORTHOGRAPHY. § 7 

Many writers have endeavored to devise rules for dividing 
words into syllables, and the result has been infinite con- 
fusion, inconsistency, and disputation. Goold Brown, in 
criticizing one of these codes of rules, says of its author: 

" He befooled the Legislature of Massachusetts, the School 
Committee and Common Council of Boston, the professor of 
elocution at Harvard University, and many other equally 

wise men of the east He would conduct the learner 

through the following particulars, and have him remember 
them all: (1) Fifteen distinctions respecting the classifica- 
tion and organic formation of the letters. (2) Sixty-three 
rules for the sounds of the vowels, according to their relative 
positions. (3) Sixty-four explanations of the different sounds 
of the diphthongs. (4) Eighty-nine rules for the sounds of 
the consonants, according to position. (5) Tzventy-three 
heads, embracing a liundred and fifty-six principles of accent, 
(<i) Ticenty-nine rules for dividing words into syllables. 
(7) Thirty-tJirce additional prineiples, which are thrown 
together promiscuously, because he could not class them. 
(S) Fifty-two pages of irregular words, forming particular 
exceptions to the foregoing rules. (9) Txventy-eight pages 
of notes." 

The foregoing quotation will serve to exemplify the diffi- 
culties to be expected by any one that tries to clear up this 
complicated subject. As a general rule that is the product 
of practical common sense, the writer suggests the following 
from Dr. Lowth: "The best and easiest rule for dividing 
the syllables in spelling, is, to divide them as they are natu- 
rally divided in a right pronunciation, without regard to the 
derivation of words, or the possible combination of conso- 
nants at the beginning of a syllable. " 

To this, however, as to every general rule, there are very 
many exceptions. 

13. Syllabication in Spelling. — The syllabication of 
words becoines a very important matter in the teaching of 
spelling, either oral or written. This Was even more the 
case a quarter of a century ago than it is now. It was then 



§7 PEDACiOGICS OF ORTHOGRAPHY. i; 

the practice to' require pupils to spell and pronounce the first 
syllable, spell and pronounce the second syllable, then pro- 
nounce as much of the word as had so far been spelled, and 
so continue until the entire word was spelled and pronounced. 
Thus, the word coDibinatiou would be spelled orally as fol- 
lows: c-o-iii, com; b-i, bi, com-bl ; ii-a, iid', cdin-bi-)ia ; t-i-o-n^ 
shfiii, cdin-bi-na -shun. 

In the case of very long- words, especially when a lesson 
contains many of them, this method becomes intolerably 
tedious and wasteful of time, with no compensatino' advan- 
tage. Educators, therefore, have from time to time in\ged 
many modifications of the old method ; so that now the 
general opinion is that the pupil, after having heard a word 
pronounced by the teacher, shall proceed as follows: 

1. Pronounce the word. This shows that he has rightly 
understood it. 

2. Mention the letters in their order, indicating by pauses 
the articulations. 

3. Pronounce the word, giving the accent correctly. 

Thwa^i combination should be spelled as follows: (1) '' Com- 
bination ; {'I) c-o-m (pause) b-i (pause) n-a (pause) t-i-o-n ; 
(o) cojn-bi-na'-tion." 

Hi spelling- hyphenated words, or words beginning with 
capital letters, their character as such should be indicated. 

Thi:s, I'^ranco-Pi-nssian, after being pronounced by the 
pupil, should be spelled in the following manner: " Capital 
F-r-a-n (pause) c-o (pause) JivpJtcn (pause) capital P-r-u-s 
(pause) s-i-a-n ; Fran-co-Pnis-sian.'' 

Lessons in syllabication should frequently be given. In 
such lessons, words shoifid be spelled by writing them at 
dictation and the syllables should be separated by hyphens ; 
as, scp-a-ra'-tion, op-por-tn'-ni-ty. The accented syllable, 
too, shoidd lie marked, for this is a matter of as much 
importance as syllabication. 

If such exercises be persisted in, the accent and the division 
into syllables will soon engage the pupil's attention just as 
much as the mere' order of the letters, especially if faults 
in any one of these respects are treated as errors. By this 



18 PEDAGOGICS OF ()RTI1()(;RAPI1Y. §7 

method, such rules as there are will i^radually formulate 
themselves in the minds of the pupils, and a general accuracy 
will emerge as the product of habitual painstaking. 

13. Illicit Assistiiiice l)y the Teaelier. — Much of the 
usefulness of spelling exercises is often destroyed by the 
teacher's method of giving out the words. Words should be 
pronounced for spelling exactly as in correct conversation. 
Certain of the vowels have what are called obsciwc sounds, 
and these should be pronounced as obscure. No attempt 
should be made to suggest a doubtful letter by a faulty pro- 
nunciation ; as, in-com-pat'-/-ble and ir-rep'-c7-r^?-ble or 
\Y-)'i'-J^dr'-a-h\e for in-com-pat'-i-ble and ir-rep'-a-ra-ble. 
Pronoimce words naturally and correctly, just as you 
would in speech, 

14. Necessity for Kxact tiiid Uiiiforiu Metliods of 
Oral and "Written Spell in j>'. — Every teacher is aware of 
the diffiictilty there is in securing, in an oral spelling exercise, 
uniformity of procedtire on the part of the pupil. Thus, if 
the teacher requires that before and after spelling a word 
the pupil shall pronounce it distinctly, the requirement, 
unless constantly in.sisted upon, is ignored. Finding this to 
be true, there are three courses, any one of which is open 
to the teacher: (1) Omit to notice the failure of the pupil to 
meet the rec[uirement. (2) Call his attention to the require- 
ment and wait until he has obeyed. (3) Treat it as an error 
and pass the word to the next pupil. 

Which of these three courses is usually pursued ? The first, 
because it is the least troublesome to the teacher. But it 
is in such trivial matters that general carelessness and want 
of painstaking find a fostering encouragement. Insistence 
is the price that a teacher must pay for accuracy, exact 
scholarship, and prompt obedience among his pupils. 

Of the other methods, which is the better ? Undoubtedly 
the last ; for, if the teacher is compelled to say ' ' Pronounce 
the word," to almost every pupil, the task quickly becomes 
onerous, and the pupil inevitably comes to wait for the order. 
In this case, it is the teacher that must be closely attentive, 



§7 PEDAGOGICS OF ORTHOGRAPII V. 1<) 

while disci])linc requires that this should be the pupil's duty. 
Even if a pupil has given the letters and the syllables cor- 
rectly, and has neglected t(^ pronounce as required, the 
teacher's unexplained "Next" should be the emphatic com- 
ment on the pupil's carelessness. In a very short time, the 
good results of the teacher's insistency will be apparent. 

The same exactness should be ob.served in written spelling. 
In school, directions of every kind .should be very brief, very 
explicit, and very necessary. And then they should be 
obeyed with military promptness and completeness. 

15. Snccess of Any Method I>epeiKleut Upon IIoav 
It Is Used. — The writer feels justified in amplifying some- 
what this point. No good teacher is wordy and vacillating. 
No good teacher issues many and complex orders that are 
changed from day to day. He makes up his mind very 
carefully about what requirements are wise, necessary, and 
defensible; then he insists upon exact compliance. It is not 
meant that he should be a iiiartiiict ; for the requirements of 
a martinet are generally luireasonable, oppressive, and inde- 
fensible. The teacher should be a disciplinarian whose orders 
are in calculated furtherance of some definite and desirable 
object. A disciplinarian never issues orders designed only 
to show that he is in authority; he has no artificial means of 
making himself heard in spite of the inattention and disorder 
of his pupils — upon his desk no bell to bang and clatter, no 
stick with which to pound desks, and, incidentally, pupils ; 
he talks but little, and then quietly ; he .says less, rather than 
more, than he means. He never scolds or threatens ; he rarely 
promises, but if he does, he performs more than he promises. 
With him, speech is indeed silver, and silence golden. 

We are not to judge, therefore, of the worth of any par- 
ticular method of teaching spelling or any other subject, by 
its success or failure in any given case. A teacher perfectl}^ 
equipped in every respect can never fail entirely, whatever 
the method maybe; the teacher having no fitness, natural 
or acquired, will certainly fail with the best possible of 
methods. It is to the teacher of no special excellence or 



20 PEDAGOGICS OF ORTHOGRAPHY. g 7 

want of excellence that modern and improved plans of pro- 
cedure are valuable. And the fact is that most teachers 
belong in this class, and herein lie the necessity for, and the 
value of, professional training of teachers. It needs scarcely 
to be remarked that the perfectly qualified teacher will be 
thoroughly informed about everything that is latest and best 
in the matter and methods of his art. 



MODIFICATIOX OF WORDS. 



COMPOITNDIXG OF WORDS. 

16. Perplexiiii? Natiii-e of the Subject. — Of the 

many questions concerning the correct use of English, there 
is no question quite so perplexing as that having reference 
to the compounding of words. Two or more words may be 
so closely associated in their meaning or use as to require 
their union also in form. This may be done either by wri- 
ting them together as a single word, called a solid coiiipoiind, 
or by using hyphens to join them. In this latter case, we 
have a liypJicncd or hyphenated compound. 

Solid Compounds. — Mankind, earrings overcoat^ hem- 
isphere, electrometallnrgy, mnltinii/lionaire. 

Hyphened Compounds. — Self-respect, ronnd-sJunildered, 
giant-killer, Jack-d-the-lantern, an P m-xviscr-than-yon 
expression. 

Evidently, there are only three ways in which two words 
maybe written: separately, with a hyphen between them, and 
as one solid word ; as, cJinrch bell, chnrch-bell, chnrchbell ; 
post man, post-man, postman. To determine, in any case, 
which of these forms is best is not by any means a sim- 
ple matter; for the closeness of association between words 
used together in speech or writing is of every degree, and 
does not remain constant. Moreover, when it is determined 
that any two parts of speech should be written as a solid or 
a hyphened compound, or that they should not, it does not 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 21 

follow that every two other words belonging to the same 
parts of speech and used in the same way, should be similarly 
compounded. This is something that depends upon usage, 
and usage changes with time and varies with locality. 

When Fulton brought forward his great invention, then the 
word steam and boat began to be spoken and written much 
together, but they were at first regarded and pronounced as 
two words. By and by, the fact of their very frequent asso- 
ciation led some one to write them with a hyphen, and the 
accent fell strongly upon the first element. Later, the 
hyphen was dropped out, no one knowing just when or by 
whom, and st cam-boat became steamboat, after which there 
was no change. This, in general, is the history of the com- 
pounding of words. 

Doubtless, if some other means of conveyance shoujd take 
the place of the steamboat, sooner or later steam-boat would 
reappear, and finally we should return to steam boat. This 
is to say, words often have a history very similar to that of 
men and women. To say nothing of their birth and death — 
their appearance and disappearance — two words may meet 
and become acquainted ; then, by means of a hyphen, a bond 
of union may be established between them — they are engaged ; 
the hyphen disappears and they are married. After marriage 
may come, for good reason, separation, and this may be suc- 
ceeded by divorce. In other words, a living language is 
constantly going through a process of change, just as is true 
of almost everything else. What is in accordance with the 
"best usage " today is displaced in a brief time by something 
else. And, in the case of two closely associated words, the 
transition to the hyphened, and finally, to the solid, form — 
how is any one to know just when it should or does occur ? 

It was stated above that usage varies with locality. The 
English spoken and written in England is in many respects 
different from that of her colonies, and from that of the 
United States; and, in the United States, there are in the 
various sections great differences in the language of even 
cultivated people. What is considered good usage on the 
Atlantic Slope is not so regarded on the Pacific Slope; and 



22 PEDAGOGICvS OF ORTHOGRAPHY. § 7 

the language of educated people in the North differs much 
from that of the same class in the South. 

17. Rules for tlie Compounding of AVortls. — Many 
grammarians and lexicographers have endeavored to for- 
mulate rules to regulate the compounding of words, but, 
unfortunately, no uniformity has been reached. Such rules 
as they have given us have been rendered practically worth- 
less by a multitude of exceptions such that no person can 
say with any certainty whether a given case belongs under a 
rule, or whether it is determined by one of the exceptions. 
If there were somewhere a literary autocrat from whose 
decisions no appeal was allowed, or if there were but one 
dictionary universally regarded as authoritative, and if tliat 
dictionary were entirely consistent with itself, the trouble 
would be ended. But there are many autocrats — self -con- 
stituted — and there are many dictionaries at war with one 
another and each inconsistent with itself. Each autocrat 
and each lexicographer believes in his own infallibility, but 
the confidence of the world is divided among them. 

One of the latest and best of our dictionaries devotes much 
attention to the subject of compounding words, and, in the 
course of a carefully prepared article concerning it, says: 

"English books contain a large number of compound 
words — that is, words made by joining two or more simple 
words into one, either with or without hyphens. The forms 
in question have never shown any real system. Many terms 
that have joint forms in some books are printed in others as 
two or more words, and exactly analogous terms often appear 
in diflferent forms in the same book. " 

The author of the article then quotes from "a recent 
book, published by one of the best-known American houses," 
such forms as the following: scJiool-roovi, scJioolroovi ; 
middle-finger, middle finger ; circus-actor, circus actor ; 
bureaii-drazver, cabin ivindoio ; back-parlor, back windows; 
and then, from the same book, gives as "compounds with- 
out reason " such hyphened forms as front-yard, top-seat, 
tallow-candle, etc. 



§ 7 PEDArxOCxICS OF ORTHOGRAPHY. 23 

Continuing, the author says: 

"Dictionaries profess to be records of the language as 
found, and not to set forth theoretical opinions; but, with 
such diversity of treatment in literature, every lexicographer 
has had to make some choice of form for each word-pair indi- 
vidually recorded Close examination of the various 

dictionaries fails to disclose any probable principle of selec- 
tion Whatever may be said, the fact remains 

that the dictionaries have given many terms as compounds 
that are not commonly so printed, and for whose joining no 
reason is apparent." 

The author then gives terms culled from the large diction- 
aries, and intended to illustrate compounds "for whose join- 
ing no reason is apparent. " Some of them ^.re good-bchavio?', 
old-maid, Frciicli-ho)icy suckle, through-ticket, clectric-curroit, 
etc. He attributes the confusion to "neglect to investigate 
and lay down correct principles and to formulate comprehen- 
sive and adequate rules." He then proceeds to do this diffi- 
cult and necessary work. 

18. Granimatical Iliiles and Established Usage. — 

After such an introduction by the editor of the subject of 
compound words, it might be expected that the dictionary 
referred to would furnish a system of perfectly definite and 
comprehensive rules, easy of application by persons of ordi- 
nary education. But, while it must be conceded that no 
more careful and painstaking attempt to solve this difficulty 
has ever been made, it is certain that the result is by no 
means satisfactory. After "a close study of English litera- 
ture " by the editor, he gives us "a system constructed /// 
accordaucc with the rules of grauimar, viodified sou/ezohat 
by such fully established usag-e as does not follow those 
rules." 

His rules are three in number, with numerous, confusing, 
and arbitrary excepti(jns. Before discussing the results he 
has reached, it may be well to note the vagueness and imcer- 
tainty of the " system ' upon which his rules depend. Per- 
haps the editor would be puzzled to explain with precision 



24 PEDAGOGICS OF ORTHOGRAPHY. § 7 

what he means by the phrase "in accordance with the rules 
of grammar" and by "fully established usage." 

It might easily be shown that many of the best grammati- 
cal authorities are still disputing as to whether or not there 
are or should be any "rules of grammar," and, if there are 
such rules, how many there are, and to what they refer. 
The following cpiotation wnll exemplify the truth of this 
statement : 

" The English language being almost without the former (inflections), 
and therefore equally without the latter (syntactical construction of 
sentences), its use must be, in a corresponding degree, untrammeled 
by the rules of gratiniiai\ and subject only to the laws of reason, which 

we call logic But the truth of this matter is that, of tlie rules 

given in the books called English Grammars, some are absurd and the 
most are superfluous. For example, it can easily be shown that in the 
English language, with few exceptions, the following simple and 
informal relations of words prevail: 

" The verb need not, and generally does not, agree with its nomina- 
tive case in number and person. 

" Pronouns do not agree with their antecedent nouns in person, num- 
ber, and gender. 

" Active verbs do not govern the objective case, or any other. 

" Prepositions do not govern the objective case, or any other." 

— Richard Grant White. 

And in the same strain this writer continues to question 
the necessity for grammatical rules, and even the existence 
of such rules. 

With regard to the editor's ' ' fully established usage, " it may 
with much confidence be asserted that there are few English 
expressions more vague and uncertain than this. What one 
authority may assert to be "fully established usage" in a 
particular place and at a certain time, another authority 
equally good, and differently situated in time and place, will 
condemn. And again, if it could be definitely determined 
what is fully established usage, and what is usage not at all 
established, how shall we decide the innumerable cases 
between these extremes ? For example, we have authority 
equally good for torpedo-tubes and torpedo tubes ; readi/ig'- 
book -And. reading book ; trolley -ear and trolley ear ; map-like 
and viaplike ; frame loork, fraiite-icork, Andframeii'ork; etc. 



§7 PEDACtOGICvS OF ORTHOGRAPHY. 25 

AVho shall decide which is right? Obviously, no one; or 
each one for himself. 

10. Tlu' IJiiles Formulated. — The editor referred to 
above gives, as the result of "a close study of English litera- 
ture," the following three rules: 

1. "All words should be separate when used in regular 
grammatical relation and construction, miless they are jointly 
applied in some arbitrary way. 

2. "Abnormal association of words generally indicates 
unification in sense, and hence compounding in form. 

'.). ' ' No expressipn in the language should ever be changed 
from two or more words into one [word] (either hyphened or 
solid) without change of sense." 

20. Discussion of the I}ules. — Every rule shpuld be 
definite, easy to be understood and applied, and entirely free 
from ambiguity. Moreover, it should, if possible, be general ; 
for, if it is applicable to only a few of many cases, it is not, 
in full sense, a r^//c\ 

Now, the rides above are faulty in nearlv all these respects. 
They leave something with respect to which the judgment, 
the caprice, the general reading and literary taste, and the 
locality of each individual, enter as elements in applying the 
rules. 

Thus, in the first rule, few people will agree as to exactly 
what is meant by "regular grammatical relation and con- 
struction," and "arbitrary Avay " is equally vague. One 
person will regard as arbitrary that which to another seems 
regular; and, worse than this, there is no acknowledged final 
authority to determine which is right. 

The second rule seems to be nothing more than an exten- 
sion of the last clause of the first rule ; for, with respect to 
words, " arbitrary application " and "abnormal association " 
will not, to the ordinary inquirer, seem very different in 
meaning. And, again, there are many degrees of abnormal- 
ity and arbitrariness in the association of words, and it is this 
" unification in sense " referred to in the .second riile, that by 
its innumerable grades of closeness makes much of the trouble. 



20 PEDAGOGICS OF ORTHOGRAPHY. § 7 

Tlie third rule would entirely prevent rail i^'ay, child like, 
uu'll coiiu\ siDi sliiiic, milk maid, etc., from ever becoming 
railicay, child-like, childlike, etc. ; for it is certain that the 
sense of sun shine, sun-shine, and sunshine is, to the ordinary 
reader, the same in all the forms. 

Of his first rule, the editor says that it "keeps a regular 
adverb separate from the adjective it modifies, even when the 
two express one attribution; as, highly colored loings, 
recently published book"; and yet the editor has best-kno7un 
in the second paragraph of his article. (Are colored and 
published, as here used, adjectives ?) 

He then says, "The second principle reijuircs compounding, 
when two adjectives, a noun and an adjective, or any two or 
more parts of speech are abnormally associated ; as, a %\.'ell- 
knoion man, the snow is knee-deep, free-trade doctrines, etc." 
Now, the information would be helpful, if any one could tell 
why loell-known should differ from highly colored and recently 
published when each combination is used as an adjective. 
Besides, it is not clear why, after what the editor says of the 
necessity of keeping a regular adverb (whatever that may 
be) separate from the adjective [or participle ?] it modifies, 
he should give us %vell-educatcd, loell-pleased, ill-treated, 
ill-supplied, and many similar forms that might be cited. 

It should be noted, however, that the editor attempts at the 
close of his article to discount criticism of his work. His 
words are, "Care has been exercised to make the vocabulary 
and the text agree throughout ; but, as many compounds 
are properly written with or without a hyphen, and as this 
is the first systematic attempt in this direction, it is not at 
all likely that absolute agreement has been attained." 

The editor is in error in saying that his "is the first sys- 
tematic attempt " to reduce the compounding of words to 
definite rules. There have been many such attempts. 
Goold Brown devotes a number of pages in his "Grammar 
of English 'Grammars" (see pages 184-193) to the subject, 
and at about the same time (1850) John Wilson gave a very 
careful treatment of compound words in his work on " Punc- 
tuation." 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. ^7 

31. Inconsistent Forms of Conlpo^ln(l AVords. — Not 

so much to show how the effort discussed above has failed, 
as to make clear to the student the great difficulty of this 
subject, the writer gives the following forms from the 
cHctionary in which the editor's work appears: fooi-bcnch, 
foot-rest, footstool; foot-ivoni, footsore; foot-pace, foot-path, 
footfall, footsteps footiuaj'; head-rail, headboard; head-band, 
headstone, head-note, headlight; hand-lathe, handbreadth, 
handsereio, handioriting, Iiand-glass, liandbook, handbraee ; 
candle-power, candle-light, candle-snuffer, candlestick, 
candleuiold, candle-end. 

The following are names of ])lants : horse-bane, dogbane, 
horseradish, horse-bean, horse-nettle, horsebrier, horse-balm, 
horseniint, horse-thistle, horse vetch, Jiorscivccd; candle-tree, 
candleberrv, candle-rush, eandlenut ; hobble-bush, rose-bush, 
feverbush, etc. 

Doubtless there are, for the editor to whom we are 
indebted for the foregoing fcjrms, some principles that 
guided his selections; but, if there are, they are too technical 
and not sufficiently obvious to be of general practical value. 

33. Evolution of Compound Words. — It is stated 
elsewhere that the changing of two or more words from 
separateness to a hyphenated or a solid compound is a 
gradual — an evolutionar}^ — process. The rapidity with 
which the transition is made depends upon many and vary- 
ing conditions, and it is not the same for all sections and 
literary centers. It is a process that is not arbitrarily deter- 
mined by any known and generally recognized authority. 
The best dictionaries have much to do with the matter, but. 
since no two of them agree, and since no single dictionary 
can be foimd that is self-consistent throughout, other deter- 
mining forces are operative. Something similar to this is the 
fashion of various articles of dress. There is no one whose 
duty or privilege it is to say what shall be the styles for next 
year. They seem to be the resultant of many forces acting 
in different directions; or, as is the case with the electric 
current, they take the path of least resistance. It is certain 



2H PEDAGOGICvS OF ORTHOGRAPHY g? 

that, with words as with fashions, "old things pass away, and 
all things become new." In the progress of civilization, 
new articles of luxury or convenience are constantly appear- 
ing, and are quickly rejected, or they become necessary, 
and, soon, indispensable. Examples of this are new forms 
of clothing for greater comfort, means of more rapid com- 
munication in business and social intercourse, and myri- 
ads of inventions of every kind. With these come innumer- 
able new names, some of them consisting of single words, 
others of two or more associated wcn-ds; as, r a ilii'ay -tele- 
graph, eottoii-giiij spiiiiniio--Jeii//j\ overeoat, overalls, postage- 
stamp, siiiokiiig-jaeket, night -goicii, torpedo-tube, ti olley-ear, 
elothes-Iiorse, baiik-aeeoitut , rubber stamp, lai^'-abidi)ig, 
ineeuse-breat/iiiig, etc. 

These terms, which at first arc rarely encountered, soon 
become familiar to the ear, eye, and tongue of almost every- 
body-. When they consist of two or more words, a process 
is begun of concentrating the accent upon one of the ele- 
ments. Thus, at first, everybody would say steam' boat', 
rail' road' , lauds' mau', ser'iwrut girl', etc. ; but very soon 
come steaui'-boat, rail' -road, lauds' -man, ser'vaut-girl, etc. 
— forms joined l)v a hyphen and having one primary accent. 
Finally, some of them take the solid form, and which shall 
do so seems to depend much upon the frequency with which 
the unaccented element is found in other compounds. 
Thus, man, fish, iceed, ivort, luay, road, and some others 
are generally added to the accented part without a hyphen; 
as, salesman, sunfish, doori^'eed, motherzcort, traun^'ay, etc. 

"itW, Pi'iniai'y and Secondai\v Accents. — Besides the 
primary accent of compounds, we usually find at least one 
secondary accent, which becomes more and mc^re indistinct, 
and often disappears entirely. In this last case, the com- 
pound takes the solid form; as, no'blemau, con'gressman, 
eod'fish, rat'tlesnake, icood' laud, etc. 

Many compounds have become solid even when the sec- 
ondary accent is quite noticeable; as, nev" ertheless' , uot"ioitli- 
stand'iiig, zidien" soev' er, ev' erybod"y, i^'hith" ersoev' er, etc. 



§T PEDAGO(;iCS OF ORTIKXiRAPHV. 2'.) 

Some writers on this subject have endeavored to make the 
compounding of words depend entirely upon accent, and, if 
their rules were expressed in terms as comprehensive as 
possible, they would be nearly as follows: 

1. If two or more words denote, not several ideas, but 
one compound idea, and if there remains but one primary 
accent, either use the hyphen or write them as a solid com- 
pound; as, for example, a matter -of 'fact' -looking town, an 
oiit-of-tkc-ioorld' place, a case of didin-kiurw-it-i^'as-load' cd, 
a sea' side residence, sjiiii mcr-ivard^ cv' cryi^'Iicrc^ etc. 

■I. If each element of a compound word retains its own 
accent, either use a hyphen or write tlie elements sepa- 
rately; as, an all' -wise' Creator, a self -eonfessed' swindler, a 
sheep' -raising speculation, a ivell' ed'ueated man, etc. 

The student will doubtless see the uncertainty attending- 
the application of tliese rules, and indeed of any others that 
may be given. It is clearly impossible to devise any rules of 
general application. This is owing to many circumstances, 
among which are the varying degrees of closeness of the 
associated elements of compound words, the distinctness 
with which the original accents are retained in the compound, 
the length of the united parts, the nature of the sounds at the 
united extremities, the grammatical functions performed by 
the compounds, and many other con.siderations. Thus, we 
may write ranilnnv and perhaps raindrop, but not raiiiclond 
or reiinconipeller; nightfall, nighteap, or night-blooming, but 
not nighttime or night-shade; a bine-eyed girl, or the girl 
was blue eyed, but not a blneeyed girl, etc. Indeed, since 
taste determines u.sage, and since taste constantly changes, 
both in individuals and in societies, there is no fixed usage 
by means of which doubtful questions may be decided. 
Everything relating to this matter is in transition. Just at 
the present time, our literary authorities are divided as to 
whether we should write today, tomorrow, and tonight with 
or without hyphens. A usage that seems to be rapidly 
increasing gives the words without hyphens, but no one can 
predict with any certainty what form the words will finally 
assume. 



:jO PEDAGOGICS OF ()RTlIOGRi\PIlY. §7 

^4. Coiu'liuliii^*' Ileiiitirks on Coiiii)oiiud AVords. — 

While it seems to be impossible to formulate definite and 
comprehensive rules for forming compound words, there are 
some general principles that may, with profit, be observed. 
Some of them are as folknvs: 

1. Uiiiu'ccssarj compounds should be avoided. — The genius 
of our language is to keep its words separate as far as possi- 
ble. When the thought can be expressed just as definitely 
by words as they are, it is not in the best taste to make new 
compounds. Of course, compounds that have been made 
familiar by use may, for the most part, be used without hes- 
itation. The Germans have a method of imiting many 
words into single adjectives, adverbs, and nouns. In these 
they use no hyphens. During the last twenty years, our 
newspapers have contained adjectives made in this way, 
except that they are formed with hyphens. They are 
apparently intended to produce a humorous effect, but they 
are not in good taste, and are a grotesque departure from 
the English idiom. An illustration follows: " He had an 
rm-aivfuUy-linnij;rv-hnt-I-caift'Saij-i\.'ood air about him. " 

•I. When several woi'ds are used to express a compound 
idea, and usage has not fixed the form, the words written 
separately are preferable to either the hyphenated or the solid 
compound. — When the solid form is admissible, it is better 
than the hyphenated compound. The reason for this is that, 
when a compound word has acquired a recognized solid 
form, no further change is possible unless the word is 
resolved into its elements, and this is very rarely done. 

3. Use the hyphen, if to do so is in any ease the only -way 
in whicJi to avoid ambiguity. — There is, however, usually 
some other way to make the meaning definite, and the com- 
pounds may then be avoided. 

The following are all ambiguous, and the hyphen is not 
the best remedy: a black bird feather, a sharp pointed tool, 
silk dress trimming, edible birds' nests, English baby stock- 
ings, many colored v\hhon<?<, one armed ■>.o\([\er, the linen paper 
box, etc. 

The foregoing can easily be made unambiguous; thus, a 



§7 PEDA(iO(TlCS OF ORTIKXiRAPHY. 31 

black feather of a bird, a feather of a black bird, a feather of 
a blackbird, a blackbird's feather; a tool with a sharp point, 
a sharp tool with a point, a sharp-pointed tool; etc. 

4. .{void coinpoiiiids having many icord cliincnts; as, a 
never -to-be- for got ten experience, a thoronglily-dyed-in-the- 
ivool democrat, etc. These may generally be avoided by 
putting' the modified word first; as, an experience never to 
be forgotten, etc. 

5. Do not pnt too nineli stress on any partienlar dietionary; 
but in each case consider the structure, meaning, and use of 
the words expressing a compound idea. 

6. Greek eonipounds and Latin eonipounds should have the 
solid form, unless there are imperative reasons otherioise; as, 
for example, pleuropneumonia, nitroglyeerin, microphotogra- 
phy, multiaxial, ambidexterity, eireumainbulate; etc., 

The writer has dwelt with considenible minuteness upon 
this subject because it is not only difficult, but very impor- 
tant. It is a subject that shoiild engage the teacher's most 
careful attention, and he should endeavor to have his pupils 
acquire a taste and an ability in the discrimination of forms, 
and in a power of giving definite reasons for preferences 
in particular cases. They should be taught to scrutinize 
hyphenated compounds, and to determine whether the sense 
may not be expressed equally well or even better by their 
separate elements. They should be trained to a careful 
conservatism as being the correct attitude when the use of 
compounds is concerned. While this is a subject that will 
never be settled, it is one of the best to furnish the extremely 
valuable discipline that results from careful discrimination. 



AHBRE>'rArrOX8 AND COXTRACTIOI^S. 



FOR>r AXT) PlXt TUATIOX OF ABBRE^'rATIOX.*!. 

35. General Statement. — It is surprising how many 
important matters there are that have never been reduced to 
comprehensive scientific rules. One of these is the subject 



32 PEDAGCHtICS OF ORTHOGRAPHY. §7 

of abbreviations and contractions— a subject of much prac- 
tical importance, and one that no alert teacher can afford to 
ignore. One might expect that the necessity of using these 
shortened forms would soon lead to uniformity, but such is 
not the case. Indeed, it would be difficult to mention any- 
thing in which is found a greater variety of usage. The 
dictionaries differ in the matter of abbreviations for even the 
commonest measures employed in business. There is 
nothing settled about their forms, whether or not certain of 
them should begin with capitals, and how their singulars and 
plurals should dift'er. Thus, we find f, ct., c/s., for ciiits; 
(/., da., das., for day ox days; in., mo., moii., vios., iox nioutJi 
ox months; ft>, lb., lbs., iox pound ox ponnds; etc. 

Some authorities insist upon initial capitals for most 
abbreviations, and upon periods after nearly all contractions. 
No attempt seems to have been made to formulate general 
rules, or rules with the fewest possible exceptions ; if there 
has been any such attempt, it has not been generally known 
and its results accepted. To realize the truth of the fore- 
going statements, one has only to observe the hopeless 
confusion in the treatinent of this subject by the various 
dictionaries. The person making an examination of the 
subject will be surprised at the great number of abbrevia- 
tions that no one uses, and that no one should use. These, 
of course, should have no recognition. In one of our latest 
dictionaries we find trans., nni., L., S., s., na., o., O., com.. 
Com., c, C, etc. To show how indefinite and empty of 
exact meaning some of these shortened forms are, it may be 
mentioned that the dictionary from which these are copied 
makes c. stand for seventeen different words, and C. for 
sixteen. Without the help of significant surroundings — 
context — such abbreviations are meaningless; but, with the 
help of the connection in which they occur, they often become 
very definite. In such connection, a Hebrew or a Sanskrit 
character would be just as intelligible; for it is the context 
that fixes the meaning of the character in such cases, and 
the character itself has no meaning. This is illustrated by 
the dashes employed by teachers in grammar exercises, where 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 33 

adjectives, verbs, or other parts of speech are to take the 
place of the dashes in such a way as to make sense. 

26. Use and Abuse of Abbreviations. — It is well 
understood that in a letter to a friend it is discourteous to 
employ abbreviations unless they are authorized to such 
a degree as to be regarded as if they were entire words; as, 
////., Sat., Oct., '98, rcsp., etc. Even these are better writ- 
ten in full. Numbers, also, unless very large, are to bj 
written in words rather than in figures. Custom, however, 
has authorized the use of abbreviations that are perfectly 
definite, in bills, statements, invoices, and business papers 
generally ; but, even in business letters, abbreviations, if 
used at all, should be used sparingly. If they occur in social 
letters, it looks as if the writer is not in reality a friend, and 
that he grudges the time necessary to say in full what he 
means. 

This subject should be carefully impressed upon the atten- 
tion of pupils until, if they err at all, it will not be in the 
excessive use of abbreviations. 

While it is a general rule that we should avoid, as far as 
possible, the use of abbreviations, there are some that are so 
definite and so widely known that to avoid them is to be 
peculiar and pedantic. vSuch are Mr., Dr., Cr., c. o. d., 
f. 0. b., oz., etc., mdsc, acc't, J/. A., P. O. The man of good 
taste is a " Roman when he is in Rome." In what every- 
body is agreed, he acquiesces. He must be indeed a great 
authority if he can ignore universal usage. But a man of 
good taste is careful to ascertain what is fully established, 
and, concerning matters in dispute, to use his best judgment, 
aided as much as possible by good authority. 

2 7 . What Are Abbreviations ? — From the coinposition 
of the term abbreviate (<'?'c/and brcvis, short), it may be inferred 
that an abbreviation is a sliortoicdioxxw of a longer expression. 
It follows, therefore, that a mere s}mibol or arbitrary character 
is not an abbreviation ; the shortened form must reveal its 

origin. Hence, |/, -(-, =, G, ^, cf-, 3, etc. are only symbols. 



34 PEDAGOGICS OF ORTHOGRAPHY. § 7 

But, if the full word or expression is revealed ever so faintly 
by the briefer character or symbol that represents it, the latter 
is an abbreviation. Thus, @, aa, ss, lb, £, ^/c, §, ^, m, f, 
are abbreviations, since, respectively, they denote more or 
less clearly the words at, ana, semis, librum or libra. Libra, 
account, United States, per, minim or meter, sitmmum or 
sunivia. 

28. Mixed Abbreviations. — Mixed abbreviations are 
objectionable ; this is on the same principle that forbids an 
English word from being composed of elements derived from 
two or more languages, as is the case with electrocution, 
talkative, interloper, and many others. But many abbre- 
viations, although of mixed origin, are so firmly established 
that they are no longer even criticized. Such are czut, from 
centum and zueight ; Jfth, 3d, 1st, ironi fourth, third, first ; 
the enigmatical numerals of the physicians, which are intended 
to excite wonder and reverence in the uneducated ; Jss for / 
and semis, one and a half; vijss for ] ^11 and semis, seven and 
a half; lbs., which is supposed to be the pluralized abbre- 
viation of the Latin librum — pluralized by adding s, as if it 
were an English word. Of this it may be remarked that our 
most careful writers are omitting the s as being unnecessary, 
since the plural of librum is libra, and lb. is the proper abbre- 
viation for either. The Spanish onza, ounce, should in like 
manner have oz. for both the singular and the plural, yet the 
dictionary referred to above gives the absurd ozs. for its 
plural. Exactly similar to civt. is divt. for denarius and 
weight. Denarius, the name of a Roman coin, was finally 
applied to the English penny ; hence we now have the 
abbreviation d. to denote penny or pence. The forms 3-cclled, 
100-lcgged, 6 footer are often used, although it is much better 
to write them in full. 

Perhaps the most ridiculous abbreviation of the mixed 
variety is dec., but happily it is now out of use. The t(- is 
intended as an abbreviation of ct, and the c is the initial of 
cetera in ct cetera. The writer has a textbook on language, 
used in some of our schotjls, in which he finds t{-ou for etc. 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 35 

The authorof the book is a Germ an -American, and doubtless 
was seeking our eqiiivalent for u. f. tu. , loid so ivcitcr. 

Another method of pluralizing abbreviations is to repeat 
the initial, the final, or some other letter, preferably a con- 
sonant; as, pp. ior pages, II. for lines., LL. iox laivsxn. LL.D., 
MSS. for the plural of MS. , gtt. for gittta, drops, and the 
double plural bbls. This last ought to be bl. but bbl. is well 
established for both the singular and the plural. Many 
symbols or mere characters are pluralized by adding 's with 

no period following; as, 6''s, +'s, A's or A, <^?'s, z's, /'s, ^'s, 
etc. *^ 

39. Contractions. — Nearly all dictionaries distinguish 
sharply between abbreviations that are, and those that are 
not, contractions; and it is important that the student Should 
know exactly what this distinction is, because of the differ- 
ence in pluralizing and pvmctuating them. As has been said 
above, any shortened form of an expression that is longer 
when fully written is an abbreviation ; but an abbreviation 
formed by omitting intermediate elements and drawing 
together {con, together, and tractus, a drawing) the remain- 
ing elements is a contraction. Thus, rce'd, /'//, we're, can't, 
e'er, Peiina. are contractions. They are also abbreviations, 
since they are shortened or briefer forms. It is sometimes 
impossible to tell whether or not an abbreviation is a con- 
traction, as in such cases as int., Cr., A/a., advt., etc., for 
interest, creditor, Alabama, advertisement, etc. 

The missing parts of a contraction are sometimes indicated 
by apostrophes or dashes, and sometimes not; as, rec'd or 
reed., indse., J — n Sm — //, aect or acct., zve/l, paynit, etc. 

30. The Period With Abbreviations. — We frequently 
meet the rule. Use a period after every abbreviation ; but 
this rule has many exceptions. In general usage, we find 
that Si period is never used after a contraction when apostro- 
phes or dashes take the place of the missing elements; as, 
W — m and H — y Sm-th, Ree'd on acc't. In full pay't or 
paym't, e'er, I'd, etc. lu such cases, the entire word is, on 



8<i PEDAGOGICvS OF (3RTHOGRAPHY. § 7 

account of the presence of the apostrophes or the dashes, 
regarded as having been written. 

Even when the missing elements of abbreviated words 
have no substitutes, many contractions omit the period. 
Thus, Rccd oil acct of jndsc, Full paymt is hereby neklgd, 
and similar abbreviations are often used in the hurry of 
business, but, to say the best of them, they are careless and 
unscholarly. They can, and should, be expressed in unob- 
jectionable forms. 

The abbreviations found in chemical, geometrical, mechani- 
cal, magnetic, electrical, and physical treatises generally, are 
commonly without periods. Thus, " will unite with //, 
At?, Fe, C, S, CI, and with almost every other elementary 
substance, to form stable compounds." "The formula for 
sulphuric acid is H.^SO^. " But, when a phrase is repre- 
sented by the initials of its several words, the period must 
be employed ; as, //. P. for Jiorsepozver^ F. M. F. for electro- 
motive foree, K. W. for kiloivatt (from kilo and Watt, a 
proper name), L. C. M. for least coviinon multiple, etc. 

With the metric system, the approved abbreviations are 
sq. em. or cm."', en. m. or m.'\ Kg., mg., dl, Dl., mm.'^ or eu. 
mm., etc. 

Names of societies, honorary titles, etc. follow the analogy 
of abbreviated proper names; as, K. S. 6"., for Knight of 
St. George, S. P. C. A., for Society for the Prevention of 
Cruelty to Animals. 

It would be difficult to specify all the varieties of abbrevia- 
tions, but the student's instinct will generally guide him 
aright. The writer believes that abbreviations should be 
used sparingly, and that, with the exception of such as are 
fully established and generally known, it is preferable to write 
in full. 

31. Pliiralizing: Abbreviations. — In addition to what 
has already been said about pluralizing symbols and abbre- 
viations, the following rules will be found useful : 

1. Contractions gcnfrally are pluralized in the same way 
as the entire words. — That is, if the entire word adds s, the 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 37 

contraction should do the same; if the word is from a foreign 
language, its contraction should not be pluralized as if it 
were an English word. 

2. Except as used in teehiiieal i^'orks, sviubols should have 
their meauiug, both in the singula?- and in the plural, expressed 
in ivords. 

Thus, in ordinary composition, G clef and G clefs are 
respectively better than the well known symbols, and radi- 
cal signs are preferable to |/'s, etc. In general, 

I). As between brevity and definiteness, the latter is to be 
preferred. 

The student is to notice, however, that brevity is often a 
source of definiteness. This is particularly the case in scien- 
tific treatises. Thus, mathematical reasoning gains in ease 
and accuracy by the use of symbols, and chemistry without 
symbols would be almost impossible. 



GENERAL C0:N8IDERATI0X OF SPELLII^G. 



PRINCIPLES AND >IATEUIALS. 

32. Spelling- as Taiis>iit Vears A^o. — One of the 

writer's most vivid recollections of the school work when 
there were no oi^cial critics of matter and method, and when 
all teachers were equally good — or equally bad — relates to 
spelling. There were then no refinements of psychology or 
considerations of "correlation " to interfere with the teacher's 
freedom of movement. The first thing in the morning was 
for the smallest lads and lasses to be summoned, one by one, 
to the master's knee. With Cobb's or Byerly's spelling book 
in one hand, and a penknife — there were /^//-knives in those 
days — in the other, he pointed with a blade at the several 
letters in turn, and informed the pupil that a particular letter 
was /', another </, and still another .r. The pupil's power of 
attention was distracted by the shine of the knife blade, the 
novelty of the situation, the overpowering personality of the 



38 PEDAGOGICS OF ORTHOGRAPHY. § 7 

teacher, and the perfectly irrelevant and disconnected infor- 
mation. The interview was short, however, but was repeated 
in the afternoon. After a period extending in some cases 
through the entire school term, or longer, the pupil was 
promoted into his ^'- a-b abs,'' including ba, be, bi, bo, bii, 
which some one has turned into a college song full of remi- 
niscences. Later came sea, see, etc., then blaek, craek, and 
so on to aeorn. The writer has open before him, at this 
moment, Byerly's Spelling Book, published in 183(j by M. 
Polock, of Philadelphia. (One wonders what else Mr. Byerly 
did to perpetuate his memory among men.) Day by day we 
climbed to the dizzy heights of learning — the path to which is 
at first so steep, and rugged, and thorny — but later so besprent 
with flowers, so smooth, so pleasant, if we may believe what 
the old Greek poet Hesiod says about it. Finally, we were 
face to face with such words as piisillaniviity, incompatibil- 
ity, eleemosynary, and many similar terms that were later to 
be indispensable in exchanging our grown-up ideas for those 
of our friends. Twice we "went through" the book, and 
some of us could spell all the "hard words" before we were 
permitted to see a reading book. As the angularities and 
inflexibilities were gradually eliminated from our tongues, 
who of us does not remember the pleasure and pride with 
which he spelled and pronounced words that at first seemed 
impossible to the human tongue. Inasmuch as this is more 
a physical than an intellectual triumph, doubtless a prize 
fighter's pugnacity would be enhanced by such exercises. 
Some one says that many of the names of the mighty old 
Greeks sound like claps of thunder; for example, Epa mi non- 
das, Agamemnon, Aristophanes. Much the same impression 
was made upon our young minds by those polysyllables of 
yore. 

33. The Speller's Instiuet. — Edward Eggleston, in 
the " Hoosier Schoolmaster," imagines that he finds the 
speller's instinct, with which Squire Hawkins was endowed, 
in the enormous nose of that gentleman; as if, like a rudder, 
it served to keep his mind steady through tangled vowels 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 39 

and consonants. It is certain, at any rate, that there is vSuch 
an instinct; and there is reason to believe that, wliile it is 
in some measure inherited, it is perfected more speedily and 
certainly by the old-fashioned " spelling for the sake of spell- 
ing " than in any other way. A good many years ago the 
writer had occasion to prepare one of his pupils to compete 
for admission as a cadet at Annapolis. The boy was excep- 
tionally proficient in everything but spelling; in that he was 
extremely weak. He was uncertain about the simplest and 
commonest words. He came one day, a few weeks before 
the examination, and said that he was anxious about nothing 
but spelling. What should he do ? The writer gave him 
one of those books filled with words chosen for no other 
reason than that they are difficult to spell, and advised him 
to go through it page by page, study each page until he felt 
certain of his ability to spell every word, and then to ask his 
brother to pronounce them for him, and to check each word 
spelled wrongly. He was to repeat this until no word on 
that page was missed, and then to proceed in like manner 
with the next page. The student will doubtless understand 
the reasons for this advice. The writer aimed at creating 
and developing the " speller's instinct." To illustrate, there 
are two ways in which faces are seen — as wholes, with little or 
no definite notion of the character or the relation of parts 
and /// detail giving special attention to the conformation 
and relation of the different features. Most of us see the 
faces and general outline of our friends in the manner first 
mentioned — as wholes. If asked later to describe minutely 
their physical features, we cannot do it ; yet, when we meet 
them, we have no difficulty whatever in recognizing them. 
But a portrait painter .sees faces in their details, and any 
departiire of a feature from the normal formation is exactly 
noted. Just so it is with words. The proficient speller sees 
in them tlie letters that compose them, and if, in writing 
them later, even one letter is wrong, he notes it at once. 

The young man referred to above professed himself much 
pleased with the result of the plan, and succeeded in standing 
second in a class of nearly three hundred. 



40 PEDAGOGICS OF ORTHOGRAPHY. § 7 

34. Heredity in Spelling. — Modern research seems to 
have estabhshed the fact that most aptitudes are in a meas- 
xwe inherited. Very certain is it that this is true among the 
lower animals. No code of commandments will ever make 
an honest bird of a crow, or prevent the cuckoo from usurp- 
ing, in the nest of some other bird, a place for her egg. No 
Draconian laws can be enacted that will obliterate the like- 
ness between the instincts and actions of the cat and those 
of her tiger relatives. There seems to be no doubt that a 
similar inheritance of distinguishing physical and mental 
qualities obtains with the human family. The musicians, 
painters, sculptors, poets, mathematicians, and orators of the 
world are usually indebted for their aptitudes to ancestors 
more or less remote. 

But the one great difference in this respect between the 
human and the brute is that the former may be educated, and 
the latter, except within very narrow limits, is incapable of 
acquiring new aptitudes. A carpenter may become a machin- 
ist, but no amount of ingenious training will convert a beaver 
into something different from a wood-cutter, dam-builder, 
and mason. But he that is not naturally endowed with the 
spelling instinct may acquire it in a high degree of perfection. 

35. A Maxim of Comenins. — We hear much among 
educational authorities of the Comenian maxim, "Learn to 
do by doing," but like every other rule believed at first to 
be general, this has its limitations in actual practice. 
"Learn penmanship by writing," say these doctrinaires. 
' ' No, " answers the expert teacher, ' ' there is a certain neces- 
sary training and control of the muscles that can be gained 
in no way so quickly and so well as by persistent drill move- 
ments that are not themselves writing exercises." These 
exercises are intended only as a preliminary training in cer- 
tain muscular and mental coordinations that are indispen- 
sable to rapid and correct progress in learning to write. 

In the learning of .most things, there are many necessary 
aptitudes that are better developed and perfected if they are 
subjected to a separate and special training. Each subject 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 41 

requires that some particular mental and physical functions 
shall be rendered harmonious and automatic in their opera- 
tion; and exercises intelligently adapted to the securing of 
such automatism are the best possible. Later, when this 
facility is brought to bear directly upon the subject itself, 
progress is easy, rapid, and pleasurable. Perhaps without 
knowing why, our writing teachers of long ago made our 
first copies to consist of "pothooks." 

There is, therefore, a preparatory training for spelling, as 
for every other subject comprehended in our early education. 
What matter what the words may be, provided we acquire 
a strong, impulse to look — to sec !* We must somehow learn 
to see words as artists see landscapes, or we shall never 
become expert in the spelling of our English tongue. The 
reproductive power of the mind must present words in .sharp 
relief before the perceptions, and, if a letter is missing, or 
wrong, the word must have to iis an aspect of wrongness — 
deformity. Knowing how to spell a word may without 
pedagogical impropriety take precedence of a knowledge of 
its meaning", its derivation, and its uses. 

3G. Abuse of irtilitarianisni. — AVliile it is true that, 
within the limits of our brief span of life, utility not too 
remote should be the criterion and end of human action, 
there is a growing insistence that ends shall follow immedi- 
ately upon actions; that, if we sow toda}-, we must reap, not 
"after many days," but tomorrow. What we really need in 
education is a more intelligent adaptation of means to ends, 
and a better general agreement as to which of several ends 
is the most desirable. The art of perfect adjustment of the 
forces that are to produce certain desired results, the causing 
of those forces to operate as predetermined, and the patient 
waiting that will take no denial — these are the conditions of 
real progress. 

But the inexperienced teacher is misled by the dictum that, 
while the pupil is learning one thing, he miist incidentally 
be learning several other things. "Never mind about how 
words are spelled that the child is never going to need in his 



42 PEDAGOGICS OF ORTHOGRAPHY. § n 

working vocabulary," say some of our pedagogical savants. 
They urge that difficult words must not be selected for spell- 
ing, and, in consequence, the pupil misses the training 
referred to above, which comes from the necessity of looking 
at words with minute attention. The teacher follows their 
advice, and wonders why his pupils make so poor a showing 
in spelling tests and examinations. In these tests, words are 
always chosen for the reason, not that they are going to be 
much in future demand, but because they are really difficult 
to spell. 

37. T-wo Objects TJetcrniine tlie Selection of Words 
for Sijelling;. — If among the useful, every-day words can be 
found such as are right in kind and sufficient in quantity to 
develop and perfect the spelling instinct spoken of above, 
the utilitarian educator is correct in his theory. But can 
this be done ? Perhaps; but a much better list for the pur- 
pose may hz arranged if the teacher may include in it some 
words at least that are chosen for no other reason than that 
they are orthographically difficult. The mathematician does 
not refuse to consider an abstruse investigation on the ground 
that he will probably never be able to use it in any practical 
application. It is the mathematical discipline, instinct, 
expertness, that he is after, and problems, theorems, equa- 
tions, differential coefficients, and integrations are to him 
what the appliances in a gymnasium are to an athlete. 

In every school, therefore, where spelling is taught, there 
should be a formal daily exercise, the object of which should 
be spelling pure and simple, and for its own sake. Other 
lessons with words there should be, of course, but the ends to 
be attained are in each case different. These other ends are 
many, such as making pupils familiar with synonyms and 
with their shades of meaning, their diiTerences in use, their 
opposites; words pronounced alike but spelled differently, 
and the reverse ; exercises designed to emphasize the rules 
that obtain in forming derivatives, etc. 

38. Sources of Selection. — The teacher will readily 
see that his success in teaching a knowledge of words in all 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 43 

their phases will depend very much upon the words them- 
selves. If they are wisely selected to meet the requirements 
of a clearly defined purpose, the results from their use wili 
be very much more satisfactory than if he uses a textbook 
chosen from among the many found in the market. Most of 
these contain lists in which no governing principle of selection 
obtains. Some consist mostly of words, that, in the main, 
"spell themselves"; others, of words that have no merit 
except difficulty of orthography; others again ring the 
changes on roots from the Latin and the Greek, and on the 
effects of prefixes and suiifixes. But in this matter, as in 
nearly every other, there is a golden mean, and this the wise 
and thoughtful teacher will always prefer. He will remem- 
ber that, in the teaching of English word.s, the principal 
objects in view are (1) to pronounce and spell in accordance 
with the best usage; (2) to teach such words as are generally 
current, their meaning, and their correct use. 

With these two objects in view, he will coijsider how they 
may most certainly and easily be attained. If he decides 
that the forming in pupils of the mental habit of looking 
attentively at words regarded not only as units, but as made 
up of parts — in short, the creating of the ' ' spelling instinct " — • 
will economize the effort necessary in the main work of making 
good spellers, he will direct his work accordingly. One of his 
first discoveries will be that no textbook will exactly meet the 
requirements of his school, and that these are determined by 
many varying circumstances of age, intelligence, and the 
probable future needs of his pupils as these needs are indi- 
cated by present conditions. He can make a better selection 
for his purpose than he can find already made. 

Some further remarks on the use of a spelling book in the 
classroom will be found elsewhere in this Paper. The obser- 
vations above have reference only to the teacher possessed of 
capacity, culture, and judgment. 

39. Our INTeetls With Reference to tlie Words We 
Use. — There are only three principal usjs that we make of 
words: (1) their use in speech, (3) their use in reading. 



44 PEDAGOGICS OF ORTHOGRAPHY. § 7 

(3) their use in %vriting. To use them with facility in speech, 
we must know how they are pronounced, and exactly what 
they mean. This includes a knowledge of the shades of 
meaning among synonyms and the several connections in 
which we may employ words of related meaning. The more 
scholarly, exact, and extensive our acquaintance with words, 
the more nearly may our conversation approach the finished 
classical elegance of the artist in words. The acquirement 
of such elegance is a work of many years, and one well worth 
the time and labor involved. The conditions necessary to the 
highest excellence, involving, as they do, so many natural 
and acquired mental qualities, are so unusual that we rarely 
meet a really fine conversationalist. The art of conversing 
entertainingly involves much more than a perfect knowledge 
of a large vocabulary. But a discussion of this subject does 
not belong here, although to no one, more than to the teacher, 
is a high degree of skill in this respect useful and necessary. 

In reading, unless it be aloud, a knowledge of the correct 
pronunciation of words is not absolutely necessary. But the 
mental act of reading is usually accompanied by a pronuncia- 
tion that makes some use, greater or less, of the vocal 
organs. Indeed, the quiet reading of many people has an 
automatic lip movement difficult to prevent. Even readers 
that show no such involuntary motion of the organs, have a 
kind of subconscious auditory perception of the words they 
are reading. This is evidenced by the fact of a sense of 
bafflement, of opposed effort, when they meet words whose 
pronunciation they cannot thus figure in conscioUvSness. The 
full consideration of the psychological side of this subject 
would be of extreme interest, and it is one of which the writer 
never has seen a M'ritten treatment. 

There are many degrees in which the meaning of what 
one reads is imderstood. It is conceivable that a person 
may read, either aloud or silently, without getting even the 
merCvSt hint of the subject to which the text relates. Indeed, 
it is probable that no two readers get exactly the same 
meaning' from a printed article of any considerable length. 
There are so many conditions affecting our interpretation of 



§ 7 PEDAGOGICvS OF 0RTH(3GRAPHY. 45 

what we read that they cannot possibly be equally operative 
with any two persons. Our conceptions of the meaning of 
particular words is very variable, and most readers only 
approximate the true meaning of words, and in different 
degrees. And, again, the same term is used in so many 
shades of the same general sense that its meaning must be 
determined by the context, — interpreted for himself by each 
reader. It is obvious, therefore, that in quiet reading the 
chief condition is that we shall understand the exact 7iicaiiiii^<^ 
in which the terms are employed. Tlie pronunciation and 
the spelling, while important, are not essential, for it is well 
known that no one now knows exactly how the Hebrew, the 
Greek, the Latin, and many other languages were pro- 
nounced, and yet they are read and understood, although 
their present pronunciation may or inay not be correct. 

In writing owv thoughts, our knowledge of words must be 
at once thorough and exact. Their ineaning, their spelling, 
their syllabication, and their form — that is, whether they are 
simple or compound — must give us no hesitation. All of 
these except their meaning belong in the domain of orthog- 
raphy. To communicate thought orally is very much simpler, 
therefore, than to do it in writing. Ordinary speecli requires 
fewer and less elaborate terms than written thought. 
"Writing," says some one, "is like shooting at a mark with 
a rifle — you may hit it or miss it; but talking is like playing 
at it with a hose — you are sure to hit the mark if you per- 
sist." Hence, in writing, words must be chosen with greater 
care with regard to their meaning, and they must be cor- 
rectly spelled, for "both gods and men despise incorrect 
spelling." In conversation, a man's culture or want of it is 
revealed by his pronunciation and his choice of words; in 
composition, his spelling becomes a determining factor. 
Hence, since the teacher's work is largely to prepare his 
pupils to write words correctly, many educators urge that all 
spelling exercises shovild be written. 

40. Oral and Written Spellinja:. — The question has 
been much discussed as to whether or not there should be 



46 PEDAGOGICS OF ORTHOGRAPHY. § 7 

any effort made in school to train pupils in oral spelling. 
' ' In their future life, our pupils will never be called upon to 
stand up in lines and spell lists of miscellaneous words," the 
advocates of written spelling assert ; and they seem to think 
this fact a sufficient answer to any arguments in favor of 
oral spelling. Now, if the teacher will • consider how 
promptly and habitually we appeal to one sense to confirm 
or amplify the report of another, and to deepen and 
strengthen an impression upon the mind, he will at once see 
that, if it is possible to use any other sense than that of 
sight in learning to spell, we are only employing the usual 
method of acquiring knowledge. The ear reports a sound 
to the mind, or the sense of smell an odor. At once the eyes 
and every other organ capable of lending assistance are 
called upon to ascertain the source, location, cause, and all 
possible particulars connected with the report of the sense 
first reached. As well might the eye be denied the help of 
the other senses in the acquirement of ordinary knowledge 
as to have no assistance from the organ of hearing in our 
learning to spell. This interhelpfulness of the varioiis 
senses is instinctive and universal. Even very young 
children reach for the moon seen vaguely by the eye. 

Moreover, oral spelling involves pronunciation, syllabica- 
tion, and articulation, all of which are indispensable to 
spoken language. By oral spelling, the sense of hearing 
. and the muscles of the vocal organs cooperate to strengthen 
the impression received by the mind from written spelling. 

In short, there is, then, no more reason for abolishing 
written spelling, on the ground that we talk more than we 
write, than there is for dispensing with oral spelling for the 
reason that it is only in writing that letters must appear in 
their proper order. Hence, it follows that spelling, both oral 
and written, should be carefully taught in our schools every 
day. The methods are complementary and not antagonistic. 

41. Coliiniii, Sentence, and Paragraph Spelling. — 

These same educators have been quibbling about whether 
pupils shoiild be taught to spell columns of words having no 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 47 

relation to one another, and selected only for the reason of 
their suitableness for furnishing- the pupil a valuable disci- 
pline in spelling, or whether they should spell words 
arranged in sentences and paragraphs. Inasmuch as the 
writing that pupils will do in the future will be mostly in the 
form of sentences and paragraphs, it is urged that they 
shonld, while in school, learn to write these correctly, and 
tJicsc alone. In reply to all this it may be said that the con- 
tention is not entirely true; bookkeepers, for example, in 
every department of business, very rarely write in sentences, 
and the art of composition is little dependent upon that of 
spelling. While bad spelling is a blemish, whether in 
column, sentence, or paragraph — whether it be oral or 
written — pupils get but little help toward learning to spell 
while they arc engaged in learning to compose. vSpelling, 
as is the case with every other subject, is best learned by 
itself and for itself. It is true that, to avoid monotony, the 
best teachers seek to accomplish their ends in various ways. 
While every day should have its undisguised spelling exer- 
cise, the subject may be introduced to a certain extent in 
teaching every other school study. The difficult terms of 
the history, the geography, the grammar, etc. may be writ- 
ten upon the board, or a couple of minutes at the close of 
each lesson may be devoted to its orthography. The essen- 
tial condition of teaching anything thoroughly is to make it 
prominent before the attention, so far as this can be done 
without losing sight of main issues. Teach spelling by 
columns of words, by dictating sentences, paragraphs, and 
poems, and by using the textbooks on various subjects. Say 
often to your pupils, "How is that word pronounced?" 
" How is it spelled ? " " AVhat word might be used instead 

of in that sentence?" "Spell it." "Write it upon 

the blackboard." 

43. Use of a Textbook in Teaeliing Spelling. — 

Educators are divided in opinion as to whether or not we 
should use a spelling book in the classroom. The dispute 
has arisen from the fact that the old type of manual on this 



48 PEDAGOGICS OF ORTHOGRAPHY. § 7 

subject contains for the most part only words of difficult 
spelling", and many of them are likely never to be useful in 
the pupil's future vocabulary. These considerations induced 
many teachers to give up textbooks entirely, and to select, 
for spelling, words from their books on other subjects. It 
was quickly seen, however, that words from these sources 
made collections just as objectionable as those of the old 
manuals. They were not words that were going to be val- 
uable for the actual uses of future life, and were in general 
not suited for training pupils in spelling. But this slowly 
growing dissatisfaction, both with the old-time book and its 
substitute, led to the appearance of many new textbooks, a 
few of them very good indeed. Some others, however, were 
constructed on the theory that we should teach our pupils 
the spelling of nothing but " every-day words." vSince most 
of these "spell themselves," it has resulted that pupils so 
taught regularly failed in the usual spelling examinations; 
for of nothing can the teacher be more certain than that such 
tests will involve difficult words. The best of our modern 
textbooks recognize this fact, and, while they contain the 
difficult words used in the average vocabulary, they have 
lists selected for the purpose of developing and training the 
"spelling instinct." Besides, all kinds of exercises with 
words are provided with the object of furnishing variety, 
without which spelling cannot be made interesting. 

While it is possible for a teacher, thoroughly educated, and 
having large views, to arrange a collection of words for spell- 
ing that will meet the requirements of his own pupils better 
than any collection in the market, it is certain that the time 
employed in the work might be more usefully expended in 
other directions. If he is permitted by the school authori- 
ties to select his own spelling book, he certainly should do 
so, and avoid the great labor involved in preparing his own 
list of words. 

For teachers other than the most scholarly it would be an 
egregious blunder to decline to use a spelling book. Con- 
ceding that books on orthography and every other subject are 
open to many and serious criticisms, it may be asserted with 



5^7 PEDAGOGlCvS OF ORTHOGRAPHY. 49 

confidence that they are incomparably better than any sub- 
stitute that could be supplied by the inexperienced teacher. 
For the most part, each book is made by an educator, who 
has given particular attention to the subject upon which he 
writes, although it must be admitted that many writers of 
school books have sadly mistaken their calling. This fact 
suggests that the choice of books for use in our schools is a 
matter important and difficult, and leads to the question of 
how and by whom such choice is usually made, and of how 
it might be done more wisely. 

43. Selection of Books for Use in Onr Scliools. — 

If all the books in our market on a given subject were sub- 
mitted for examination as to their respective merits, to the 
most competent untrammeled authorities, with the object of 
determining the best for use in the schools of a state, county, 
city, or district, the choice would still be involved in much 
difficulty. In the first half of our century, school books were 
few, and most of them very poorly suited to their intended 
use. Parents chose, or, rather, bought, the school books for 
their own children. The result was that graded schools were 
impossible. At the present time, our graded system has 
made it necessary that books shall be uniform, at least 
among the pupils under one general management. How to 
attain this, and at the same time obtain the books at the fair 
prices that result from competition, is a difficult problem. 
Without discussing the multitude of methods of choosing and 
buying books for the school children of our country, the 
writer wnll describe what to him seems to be the best. It 
has the merit of being applicable not only in large cities and 
towns, but in villages and country districts. 

A committee on textbooks is appointed by the educational 
board. This committee should consist of several members 
from the board, and with it .should be associated the super- 
intendent and two or more of the most capable principals or 
teachers in charge of the schools. The duty of this commit- 
tee should be to select from the many books in the market a 
list comprising for each subject several approved manuals by 



50 PEDAGOGICS OF ORTHOGRAPHY. i< 7 

different authors. In some of our large cities this list may 
include practically all the books of recog-nized excellence 
that are published in our country. These should then be 
adopted by the general board, and their various publishers 
asked to submit prices at which they would supply the books. 
When the bids have been received and accepted, lists with 
prices should be printed and sent to all the principals, or, if 
there are no principals, to all the teachers in the employ of 
the board. Upon the principal of each school should be 
devolved the duty of selecting for a period of not less than 
three years the books to be used in the. classes under his 
charge ; and he should not be permitted to change his books 
before the expiration of this period without the recommenda- 
tion of the superintendent, and for reasons that must be sub- 
mitted for approval by the board. These books should be 
purchased by the board as they may be indicated by requisi- 
tions of princijxils. Each school should be credited with 
its pro rata share of the school-book fund for the year, and 
each principal should be recpnred to keep a careful report of 
books received, on hand, lost, worn out, etc., and to submit 
to the board each term an inventory and full report showing 
all important facts relative to tliis subject. Pupils using the 
books should be held responsible for damages beyond reason- 
able "wear and tear." The advantages of this system are 
many. Chief among them are these: the books w'ill not cost 
the board more than half so much as parents would be 
required to pay for them, and the same set of books can be 
used in turn by different pupils. 

Some states, knowing the cheapness with which books may 
be manufactured, have made the experiment of employing 
authors to wn'ite their textbooks, and have printed them at 
public expense. The experiment has not, however, proved 
a good one, for the reason that it became a prey of political 
jobbery, and, in the end, cost more than to have the parents 
buy the books needed by their children. 

44. Personality of the Teacher aii Element of 
Success. — -As has already been intimated, the teacher has 



§7 PEDAGO(;iCS OF ORTHOGRAPHY. 51 

more to do with tlic success of any subject in the classroom 
than all other elements except the mental capacity and alert- 
ness of the pupil. It makes less difference than is generally 
imag'ined what spelling' books are used, by whom they are 
chosen, and bv what method; the results will be unsatisfac- 
tory unless the teacher himself is a speller, and knows how 
the subject should be taught. The great elements of suc- 
cess, after all, are enthusiasm and persistence on the part of 
the teacher. These qiudities in him will beget their like in 
his pupils, and then failure is impossible. If he is himself 
an expert speller, the presumption is that he was well 
taught, and the good methods that were pursued by his 
teacher will naturally be remembered and practiced in his 
own work as a teacher. A teacher's influence is, therefore, 
very great; for he is engaged in preparing his pupils for the 
intelligent discharge not only of the ordinary duties of life, 
but also many of them for work like his own, since many of 
them will doubtless become teachers. These will copy, 
luiconsciously, it may be, his inethods, and, if failure results, 
the failure will be largely owing to the faults of their 
prototype. 

45. Dr. Rice's Articles in " Tlie Forniii" on Si)ell- 
Ing. — In the interest of better inethods. Dr. Rice, the editor 
of "The Forum," recently made careful and instructive 
investigations and comparisons of the teaching of spelling 
in the schools of our largest cities. He discusses many 
phases of the subject and arrives at some very interesting 
conclusions. These are in the main adverse to present 
methods, and his contentions have been widely criticized ; 
nevertheless, the teacher can find in his work many helpful 
suggestions. He insists very earnestly upon the necessity 
of using in spelling exercises only such words as are likely 
to be useful in an ordinary vocabulary; but, from among 
these, he w^ould exclude those that furnish no discipline 
in spelling. He estimates the number of such words as 
require to be studied at from 6,000 to 7,000. He believes 
that, if a student has mastered these, he will have but little 



5-1 PEDAGOGICvS OF ORTHOGRAPHY. §7 

difficulty with the words that occur in the actual business 
of life.- 

As to rules, he does not favor the learning of many, since 
nearly all have a great variety of confusing exceptions. He 
makes especial mention of two that are of wide application, 
and are, therefore, very useful. On this subject he says : 

"The words that can be learned collectively are those to 
which rules of spelling apply. While, in some instances, the 
exceptions are so numerous as to rob the rules of their value, 
a few of them, nevertheless, are very reliable, at least for all 
practical purposes. And, as these rules govern thousands of 
words, it would be much less burdensome to master them 
than to memorize such words individually. Among these 
rules, two are particularly comprehensive, and should be 
taught, year after year, until applied automatically. They 
are, first, the rule refeiTing to the doubling of consonants, as 
in ru/i — running ; and, second, the rule concerning the drop- 
ping of the final c, as in bake — baking. That so many chil- 
dren, even in the highest grammar grade, should spell lose with 
two d'S, does not necessarily throw discredit on the teacher; 
but that a child after attending school four years or more 
should write 'While runing he sliped,' or 'She was bakeing 
cake,' is as unpardonable as if he were unable to add 2 and 3. 
And yet out of 252 pupils in the fourth school year, whose 
papers were examined with reference to this point, running 
was misspelled by 94, slipped by 12G, and baking by 09. 

"That little advantage is now taken of rules is indicated 
by the fact that, broadly speaking, as many errors were made 
on words governed by rules as on those to which they did 
not apply." 

In concluding his final paper, ' ' The Futility of the Spell- 
ing Grind," the same observer says: 

"Although a liberal admixture of methods and a judicious 
selection of words would be of material assistance, nothing 
can take the place of that personal power which distinguishes 
the successful from the unsuccessful teacher. Consequently, 
our efforts should be primarily directed toward supplying 
our schools with competent teachers. As the number required 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 53 

preckides the possibility of limiting the selection to those 
born for the profession, our only course lies in developing 
the requisite powers, as well as we can, where they are nat- 
urally weak. To this end, I believe that no means can be 
more effective than to prescribe a definite task, to be com- 
pleted in a given time, and to make the tenure of office 
depend on the ability to meet the demand. If my proposi- 
tion should consider the results alone, then, of course, it 
would be fraught with the danger of leading us back to the 
era of endless mechanical drill; but so long as the time limit 
is a sine qua uoii, the danger is averted." 

46. Remarks on the Foregoing;. — With much that Dr. 
Rice says the writer finds himself in accord, but he is com- 
pelled to disagree with the conclusions reached in, the last 
paragraph. The introduction of the " time limit " would not 
only fail to exclude mechanical drill, but it would lead to a 
neglect of other subjects, in order to make room for such 
drill. If, to prevent such neglect, an amount and time limit 
were fixed for every subject, rational teaching would dis- 
appear, and the method of "cramming for examinaticjn " 
would be followed exclusively. The student must not 
imagine that thoughtful educators, in the hope of reaching 
more satisfactory results, have neglected the method of limit- 
ing the time, and of specifying the amount to be done in that 
time. But the consequence always has been and always will 
be to run thj scho;)ls into mechanical drill. The fact is that, 
speaking in general terms, the teachers of our country are 
working up to the level of their best ability, and these faults 
of driving and oversupervising are always productive of 
routine work, with the obliteration of the teacher's personal- 
it}', which Dr. Rice regards as more valuable than ''methods 
and a judicious selection of the work to be done." Wliat we 
need more than this officious supervision are: the divorce- 
ment of our schools from the domination of the politician — 
this above all ; greater fixity in the teacher's tenure of office, 
so as to encourage him to look upon teaching as his life work; 
better salaries, to warrant and encourage more adequate 



54 PEDAGOGICS OF ORTHOGRAPHY. § 7 

preparation on the part of those proposing to engage in the 
work; the exaction of higher scholarship in teachers as a 
warrant for the payment of better salaries. 

Of one thing we may be perfectly certain — if a teacher can 
teach a subject well, he will inevitably do so without any 
ingenious forcing processes on the part of his employers or 
of his official superiors; if, on the other hand, he cannot teach 
successfully, no ingenious parceling out of subject matter or 
time, and none of the devices of supervision, or even the 
danger of losing his place, can make him successful. That 
supervision and planning and incentives to excellence are 
entirely without value, the writer does not by any means 
assert, but their value is much less than is generally sup- 
posed. One of the largest cities in our country is notorious 
for the utter inefficiency and worthlessness of its schools. Its 
critics and its teachers say that the schools are " supervised 
to death." These schools have a "time for everything," 
and no time for anything not indicated beforehand. Each 
teacher knows that, on a certain day of each term, his pupils 
are to solve the examples on a particular page in a certain 
arithmetic, to spell the words of a certain lesson in a spelling 
book, and so on for the other subjects. It is well known 
beforehand that the examination by the superintendent's 
representative will cover certain ground, and no other. It 
follows, therefore, that the teachers work for the coming 
examination, and not to educate and discipline the pupils. 
This school system is in the octopus-like grasp of a powerful 
political "machine," whose incompetent proteges fill all the 
best positions in the city. Every hope of reform is cut off 
until the people rise and destroy the power of the ' ' machine. " 
Even then, thousands of worthless teachers, each with a 
much more powerful support than the really able teachers 
possess, must be displaced before the good teaching that all 
desire to see will be possible, 

47. General Criticisms on the Purpose and Result 
of tlie Articles on Spellinj^-. — After reading Dr. Rice's 
articles in "The Forum," which were written in comparison 



§ 7 PEDAGOGICvS OF ORTHOGRAPHY. 55 

and criticism of the methods, matter, .and results in ''the 
schools of nearly all the large cities of the country, and after 
a careful study of the actual spelling" of more than 3o,()0U 
pupils," one feels reluctant to criticize the practical value of 
the conclusions he has reached. It is certain that the method 
of investigation he pursued is the best possible, provided 
always that the investigator has no preconceived theory to 
confirm. We all know how easy it is to find that which is in 
favor of our views, and how extremely difficult to recognize 
the existence and the force of opposing facts. If all investi- 
gators were perfectly impartial, the proper method of pro- 
ceeding in any given case could easily be ascertained; but 
the fact that few educators agree, and that new theories are 
being constantly advanced and supported by plausible, if n jt 
always good, reasons, would seem to teach that not too much 
stress is to be placed upon the inductions from investigation, 
real or alleged, of the vexed questions relating to teaching. 
As might have been expected. Dr. Rice's investigations were 
preliminary to the appearance of two spelling books compiled 
and arranged by himself. Although it would be unfair to 
assert that the end in view would naturally be influential in 
leading him to liclieve that every other textbook on spelling 
is faulty or unfit for use, there is good reason for carefully 
considering whether what he suggests is really better than 
what we already have. Before proceeding to examine his 
books, it should be remarked that somehow there are a great 
many people that are excellent spellers. It might be inter- 
esting to inquire what books they used, and in wliat manner, 
to attain their proficiency. As the Doctor suggests in one 
of his articles, books and methods have less t<j do with suc- 
cess in teaching spelling than some other things, notably 
the personalitv of the teacher — his enthusiasm, his intel- 
ligence, his ability to awaken his pupils and to inspire them 
with high ideals. A good teacher with a genius for his work 
will make good spellers with any manual or none at all, 
while a poor teacher will fail, even with an educationally 
perfect spelling book. Good tools will undoubtedly render 
a good workman's task easier, and the results better; hence. 



56 PEDAGOGICvS OF ORTHOGRAPHY. § 7 

since it is conceded that some textbooks are better suited to 
their purpose than others, it is important that the best books 
available shall be selected. 

Dr. Rice's books are excellent in many respects, but the 
writer cannot help thinking them open to considerable 
criticism. He advises that "not more than fifteen minutes 
daily be devoted to spelling-, including study and recitation.'' 
He states that his investigations have shown "that addi- 
tional time given to this subject is not rewarded by additional 
return. " The writer believes that this statement is at vari- 
ance with all human experience. Unimportant indeed must 
the subject be that is worthy of no greater expenditure of 
time. We all know that if one wishes to become expert in 
mathematics, science, language, history, or any other sub- 
ject, he must devote much time to it. Dr. Rice's lessons are 
made in accordance with his theory. He says of them, "The 
words have been divided into lessons, each of luhic/i repre- 
sents an entire 7^'eek's ivork — not counting the revieivs. The 
number of words in a lesson varies from 15 to 20." Just 
think of the monotony of work trifled with in this manner. 
His second book, intended for pupils during the fourth, fifth, 
sixth, seventh, and eighth years, contains less than o,500 
words. Counting 200 school days in a year, this will give 
an average of about 17 words a week, or a trifle over 3 words 
a day. This is nearly equivalent to not studying spelling 
at all. 

48. Diacritical Marks and Syllabication in Spell- 
ing Books. — Another striking departure by Dr. Rice from 
the usual practice is in the absence of syllabication and dia- 
critical marks. In his preface, he says that his plan " obvi- 
ates, to a large extent, the necessity for the study of pro- 
nunciation." In consequence of this, he indicates in his first 
book neither syllabication nor pronunciation, and in his 
second book, he treats in the same fashion all except 204 of 
the 3,500 words in his lists. Of course he omits all accent 
marks. Now, as is well known, there are many words that 
the average teacher cannot accent and pronounce with any 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 57 

degree of certainty without the help of diacritical marks; 
and syllabication, notwithstanding what the Doctor says, is 
a very important matter. Indeed, so far as the writer has been 
able to ascertain, there are very few spelling books in the 
market that omit the syllabication of words, and wherever 
there is any uncertainty about accent or pronunciation, dia- 
critical or other marks indicate them. It is the general 
practice, and a good one it is, to teach pupils the usual dia- 
critical marks. Without this knowledge, it is impossible to 
use a dictionary intelligently, and, in our courses of study, 
no provision is made for learning these marks except in con- 
nection with the work in spelling. Dr. Rice's opinion seems 
to be that, since in speech and in ordinary print we are 
required to know the accent and pronunciation of words 
without help from diacritical marks, we should have no such 
help in- the spelling book. With regard to syllabication, 
attention has been called elsewhere to its usefulness in pro- 
nunciation and to its great value in writing. 

It is believed, therefore, that Dr, Rice's books are very 
much impaired in working value by the omissions indicated 
above. Indeed, one may always doubt the wisdom of differ- 
ing widely and radically from that which is generally recog- 
nized. We are constantly beset by people that have made 
striking and unexpected discoveries in each of the many 
departments of human knowledge. New systems and m.eth- 
ods of procedure are based upon these alleged discoveries, 
and the public is urged to walk upon a new "royal road to 
learning." In adopting reforms, it is always wise to "make 
haste slowly," and to remember that real progress advances 
with tardy step. " Neither a radical nor a con.servative be," 
but make sure that your feet are on solid ground before 
taking tlie next step. Talleyrand said in tlie Chamber of 
Peers, "I know where there is more wisdom than that of 
Napoleon, Voltaire, or all ministers that have been or will 
be — in public opinion." This wisdom is realized in no one 
book or man, but in all. Herbert Spencer's contention that 
no doctrine or theory is utterly wrong or untrue, implies 
the oppo.sitc — that none is absolutely rig-ht and true. The 



58 PEDAGOGICS OF ORTHOGRAPHY. § 7 

iiitclli^ti-ent teacher, therefore, will believe implicitly in but 
few things, neither will he reject everything- — he will investi- 
gate, and will think and act for himself. 

49, Words ill Conmioii Use. — Dr. Rice tells us that of 
the words in common use, difficult to spell, there are between 
0,OUU and 7,000. Now a little reflection will make it evident 
that this is a matter of much uncertainty. There are three 
ways in which words are used. 

1. Words may be used in ordinary speeeh. — Of these we 
do not absolutely need to know the spelling ; for people 
that can neither read nor write employ words in speech, and 
very fluently sometimes. Of course, the more thoroughly 
we know words — their orthography, composition, derivation, 
exact meaning, etc. , the more accurately we shall use them 
in our conversation ; but we may know them well enough to 
communicate our thought by means of them, and yet have 
no knowledge of how they look in print, what letters make 
them up, their etymology, or their grammatical relations in 
our sentences. 

3. Words may be used in ivriting. — To use words cor- 
rectly in writing we must know more than their meaning 
and how to pronounce them. We must, besides, be familiar 
with their spelling and their syllabication. To employ them 
with grammatical correctness, it is necessary for us to be 
familiar not only with the principles of theoretical grammar, 
but also with practical grammar. 

3. Words iihiY be used in printed matter. — The great 
object to be attained here is to understand the meaning of 
what is read. In order to do this, the reader must be 
familiar with the meaning of the words employed; and, if 
he would read aloud, he must know their pronunciation. In 
learning these things, it would be strange if the reader did 
not meet many words not in C(MTirnon use, and get much 
knowledge of tlieir composition, grammatical properties, 
derivation, etc. In other words, we learn spelling more 
from the books that we read tlian we do from the spelling 
hook. A person in ordinary circumstances in life has for 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 5!) 

speech a very limited number of words, most of which are 
easily spelled. The same is true of the words he uses in the 
writing' connected with his business or social relations. If 
his vocabulary could be collected in its entirety, a few weeks 
would suffice to learn the spelling of all the words com- 
posing it. 

But the working, e very-da}' vocabulary of one man differs 
somewhat from that of every other man; and, if all the words 
contained in the vocabularies of the people of a country, a 
state, or even of a county, were in one collection, it would 
contain a great many thousand words. If to these be added 
the words in common use in the writings of our best authors, 
to say nothing of the thousands of words used in writings on 
the arts, sciences, commerce, and industries, the spelling 
book that could contain them would become an unabridged 
dictionary. 

What, then, is meant by the expression, "the words in 
common use," and by what means does Dr. Rice fix their 
number so definitely ? Clearly, it is one of tho.se current 
expressions carrying no particular meaning. The writer 
ventures the following assertion: A man is not a good speller 
if he is familiar with only the words he himself habitually 
uses in his speech and writing; he inust know how the 
words are spelled that other people use, including the 
myriads employed by writers on every variety of subject. 

50. Oi'tliograpliy Is Jjeai'iied More From Ileadiiijaf 
Thau From tlie Spellinj*' Book and the Dictionary. — - 

Not much need be .said, the writer believes, in proof of this 
topic. just as the u/ctuniii^s of most of the words that we 
know are learned, not from dictionaries, but from the use in 
which we hear them, and from their context in what we 
read, so their ortliograpliy becomes familiar to us from their 
printed forms. If their spelling, as seen in different places, 
varies, it is at once noted, and a wish to be certain about the 
correct form is aroused. The approved dictionary becomes 
then the court of last resort. 

In "order to learn orthography in this way with rapidity 



00 PEDAGOGICS OF ORTHOGRAPHY. § 7 

and certainty, the reader must be in possession of the 
"spelling instinct" that insists upon looking at words 
minutely, as an artist looks at a face or a landscape, or as an 
architect looks at a building. But the course in spelling 
proposed by Dr. Rice, covering as it does not more than 
fifteen minutes of daily practice in spelling the comparatively 
small number of words alleged by him to be all that are in 
common use, will never make accomplished spellers. An 
average of about seventeen new words per week, difficult 
and easy, is not enough to arouse in pupils the necessary 
interest and enthusiasm — not enough, indeed, to make them 
aware of the fact that spelling is one of their school studies. 
It is not in this fashion that scholars are made. 

51. Importance of Reading Good L/iteratnre. — If 

the foregoing remarks are warranted by the facts, and that 
they are the writer believes the experience of most will con- 
firm, the teacher will see the necessity of encouraging his 
pupils to read good literature. Dr. Johnson observes that 
no man can read much for five years without becoming a 
scholar. Skill, facility, and accuracy in the use of words, 
not alone in spelling them, but in using them to express our 
own thought, and to interpret the thoughts of others, are the 
legitimate and necessary results of reading. Indeed, it may 
be remarked in general that the schools furnish us only the 
merest rudiments of an education, a kind of key or cipher by 
means of which we may interpret the great worlds of nature 
and of thought that lie outside the classroom. 

It follows, then, that to get the best orthographical result 
from reading, it is necessary that the reader shall have his 
eyes trained so as to note minutely and accurately the forms 
of words; that is to say, he must have a well developed 
instinct to recognize and remember the orthograpliy of the 
words he meets. And it is equally certain that this cannot 
be attained in any other way than by spelling much for the 
sake of .spelling. In tliis trahiing, it is really of little con- 
sequence whether or not the words upon whicli he practices 
are all likely to be used daily in his future vocabulary or in 



^ 7 PEDAGOGICS OF ORTHOGRAPHY. (iL 

that of his neighbor. The}' may or may not. Their present 
use is for a discipline that is vahiable not merely as a means, 
but also as an end. Not every educational method must be 
wholly dominated by considerations of practical utility. 

52. Utility and Mental discipline. — It should be 
evident from what has been stated imder the preceding 
topics that two entirely different objects should be sought 
in orthographical training, and that these objects should 
determine the character of words selected for spelling, and 
the use made of them in teaching. In the first case, words 
are selected not because they are of diiiticult orthography, but 
because they are likely to be useful in the actual affairs of 
life. Tliese will comprehend the terms that ordinary pre- 
vision will indicate to be necessary for social and common 
business purposes in an average environment. Of course, 
if a pupil's future should lie among unusual activities, many 
words will have to be added to the vocabulary in which he 
is trained at school. But these will be acquired as circum- 
stances develop the need for them, and no one can determine 
in advance what additions will be required. The best that 
can be done is to approximate as nearly as possible to a good 
working vocabulary under ordinary circumstances. 

In selecting words for training in mere spelling, they 
should be chosen, as has been said, not so much because they 
are likely to be serviceable for speech and writing, as because 
they are of peculiar spelling. It is to be noted, liowever, 
that a word having value both for future use and present 
training should be preferred to a word that is only of dil^cult 
orthography. But the number in this latter class is not 
great; and there are many words of great value for training 
purposes that are of little use in an ordinary vocabulary, 
and these should be iised for spelling. If any attention is 
given to their meaning or use, their composition or deriva- 
tion, it should be very brief and cursory. Otherwise, the 
object in view in using them will be defeated, if not wholly, 
at least partially. 

The words in the first class are to be studied thoroughly. 



G;i PEDAGOGICS OF ORTHOGRAPHY. § 7 

I'hc eye should l)e niade familiar witli their forms, the ear 
witli their sound, tlie tongue with their ntteranee, and the 
mind with their meaning and use. They should be made 
so familiar to the pupil as to ineorporate themselves in his 
ordinary voeabiilary. Exereises of many kinds and of 
daily occurrenee should keep them before the pupil's mind 
until their use has beeome involuntary; and repetitions 
and reviews should be praetieed with them to the edge of 
monotony. 

53. Means of ()btaininj>- Words for Oi'tliograplilcal 
Work. — In the earliest spelling books published in this 
eountry, the prineiple of .selection was very simple. After 
a eertain number of lessons, the leading object of which was 
to familiarize the pupils with the sound of letters singly and 
in combination, the transition to words that were merely 
difficult to spell was very rapid. The probability of meeting 
or using a word in fiUure was not considered; the only 
requirement was that its orthography should be abnormal — 
the more so, the better. Books of this kind have not yet 
disappeared, and for the purpose of training explained in 
the preceding paragraph, they are of undoubted value. 
Most of the books of "Test Words" have been modified, 
however, by the exclusion of such terms as are rarely or 
never used in any modern book, but much of the difficulty 
that characterizes the earliest textbooks has been retained. 
Hence, for training in mere spelling, they serve the purpose 
excellently. It is iinneeessary to mention any of these books, 
for most teachers are familiar with some of them. Better 
than any one of them, perhaps, for a particular school, grade, 
or locality, would be a collection made by the teacher or 
principal of the school where they are to be used. No one 
can know the needs of a class so well as he that teaches it, 
if he is thoroughly capable. 

The writer must not be understood as favoring the dis- 
carding of all spelling books, and the substituting of words 
from the geography, the reader, the history, and other text- 
books. The words in those books are better learned as we 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. (;;) 

learn the words in general reading;. They do not present 
the proper degree- of difficnlty for training llie spelling sense, 
nor are they snfficientl)' practical for a working vocabnlary. 
It is trne that some of them are suited to these recpiirements, 
but with the greater ptjrtion of them, this is not the case. 
The Avriter is eonvinced that a good spelling hook is a neces- 
sity in our schools. 

Many books have lately appeared containing hsts of words 
that are excellent for their practical iiscfulncss. Thev have 
been cidled with great judgment from many sources, and 
have been divided into classes according to their spelling, 
their pronunciation, their meaning, their nse, their relation 
in sense to other words, the rules that govern their form, 
the roots they contain, their derivation, composition, etc. 
An element of much value in some of these books is that 
they outline many ])edag()gical devices. By their use the 
teacher may avoid much of the monotony and humdrum of 
the work in orthography. vSome of these books invade the 
domain of grammar t(j the extent of treating of pimctuation, 
parts of speech, the possessive case, pluralizing, capitalizing, 
paragraphing, and composition work in general. Not much 
objection can be urged against this, ho^vever; for orthog'- 
raphy is really a part of grammar, and every consideration 
bearing upon a correct iise of words is important to the 
teacher of orthography. 

54. The C'()llectinj>' of Devices for Teaching" Orthog- 
raphy. — If a teacher expects to make the profession his life 
work, it would be. difficult to overestimate the importance of 
his lieginning early to preserve in note books the plans of 
work that he finds successful. When he leaves the normal 
school he should be well supplied with hints, devices, plans, 
skeletons of work, methods of procedure, etc. These shoidd 
be in such form as to be readily accessible and available. 
A teacher depending upon general psychological principles, 
and upon pedagogical rules as he remembers them, will 
very soon become a slave of routine and mechanical methods. 
If he would have freshness and variety characterize his work, 



04 PEDAGOGICS OF ORTHOGRAPHY. § 7 

he iiiusL not depend upon his memory to reeall, or upon his 
instinet to sug-gest, the appropriate method of procedure. 
H what has been tested and found successful is made a mat- 
ter of record, the certainty of his handling a given subject or 
lesson well and wisely is assured. 

These plans and devices, many of them, will emanate from 
the teacher's practice, and more of them from his reading 
of what others have done. One of the characteristics of a 
good textbook is its richness in suggested methods, and the 
progressive teacher will therefore welcome every new school 
book; for, however faulty it may be, it will undoubtedly 
contain something of value that he can utilize in his work. 
It makes but little difference where the teacher gets a new 
plan — from his own experience, from that of other teachers, 
or even from the successes and failures of his pupils — if it is 
valuable, he should preserve it; and presently his choice of 
what is best in matter and method will become involuntary, 
just as much so as that one having the speller's instinct will 
spell a word correctly rather than otherwise. 

55. Concerning- Rules for Spelling. — Most of the 
systematic training that our children get in spelling is con- 
fined to their earlier school years. It is true, however, that 
expertness in this branch is like skill in piano playing or 
stenography — it requires constant practice. To become infal- 
lible in the orthography of our language is a life work. 
Orthography cannot be generalized under a few comprehen- 
sive rules, nor under many rules. The fact is that our best 
spellers know very little about orthographical rules; they 
simply know how to spell particular words from the fact that 
they have sir// them one by one with eyes that note what they 
see. If they happen to know the languages from which most of 
our English words are derived, so much the better; but upon 
formal rules they put little dependence. This is owing not 
merely to the fact that these rules have generally a great 
man)'- exceptions, but also to the fact that the mental effort 
necessary to apply a rule and note the exceptions is greater than 
that required to impress the many words upon the memory. 



§ 7 PEDAGOGICvS OF ORTHOGRAPHY. G5 

But, as has been stated above, the formal study of spelling 
is confined to children of comparative youth, and to them 
rules are difficult. However simply a rule may be stated, 
there is an unavoidable abstractness about it that removes 
it beyond the comprehension of young children. One of the 
authorities on this subject insists that there arc only two, or, 
at the most, three, rules that can be used with advantage in 
teaching spelling. It seems, therefore, to be best that young 
children should be taught to spell without the aid of rules. 
Even in more advanced age, it is doubtful whether much is 
gained by trying to spell by rule. Moreover, there is no 
unanimity among the various authorities as to the number 
of rules and their application. Goold Brown, whose atten- 
tion to this subject was exceptionally careful and thorough, 
gives fifteen rules, with thirty-one ' 'observations " in fine type. 
Each of his rules has many exceptions, and these, with his 
observations dealing for the most part with varieties of spell- 
ing and with its curiosities, constitute a task more difficult 
to learn thoroughly than to learn to spelL Some authors 
have more rules than Mr. Brown, and others fewer, but no 
two authors can be found that agree. Indeed, this is one of 
the many .subjects that has never been reduced to a gen- 
erally acceptable system, and it perhaps never will be. 

56. HVecessity for Drill and Ilepetition. — The reten- 
tive power of tlie mind is facilitated by three circumstances 
— vividness, rc'f>cfitio/i, and attention. In all these the 
teacher has a large determining influence. In order to pro- 
duce the greatest possible vividness of impression upon the 
mind, he may employ several of the senses. The organs of 
speech may be required to utter a word while the ear notes 
the utterance and sits in judgment upon it. The muscles 
of the hand may fashion it for the criticism and approval of the 
eyes. The eye, the ear, and the organs of speech unite in 
strengthening the impression upon the mind. But, however 
thoroughly this may be done, experience teaches that it 
should be repeated, and, in most cases, frequently. Indeed, 
other things being equal, the success of a teacher depends 



66 PEDAGOGICS OF ORTHOGRAPHY. § 7 

much upon the persistence and thoroughness with which he 
looks after his reviews. It is not safe to assume that, because 
a matter has been carefully studied, perfectly understood, and 
satisfactorily recited, it needs no further attention. Things 
in the mind have a decided tendency to lose their distinct- 
ness, and to become confused with other matters. Their 
frequent disentanglement and rearrangement are necessary. 

Again, the teacher has much to do with the degree of 
attention on the part of his pupils. His manner, his tones 
and emphasis, his personal interest and enthusiasm, the 
order in which the important elements of a lesson are pre- 
sented, the pertinency of his remarks and questions, the 
naturalness of the associations that he establishes, his power 
of illustration — these, and innumerable other conditions that 
are scarcely capable of statement, determine whether the 
pupil's attention shall be steady and intense, or fitful, slight, 
and wavering. This, however, is certain: if the impression 
is to be permanent, it must be deep; and, to insure such an 
impression, the cause upon which it depends must operate 
vividly, must be frequently repeated, and must command 
the utmost fixity of the attention. 

It may here be observed that young children have very 
little power of voluntary attention; hence, it is almost need- 
less for a teacher to make a formal verbal demand for the 
attention of a class. Even with persons of mature mind, 
that which secures attention is objective, external — not. sub- 
jective. We never say to ourselves, " Now% I ought to be 
attentive to what the speaker is about to say, for it is closely 
related to my own welfare." The same things said by two 
different speakers affect their audiences differently. One 
person reads to us a striking poem — it is not striking; 
another reads it, and stirs our deepest emotions. Similar 
differences in the power of influencing pupils obtain among 
teachers. An inattentive class should not be blamed or pun- 
ished for its inattention. The fault — or rather the misfor- 
tune — is the teacher's. But every teacher can and should 
review frequently; for, without this, even the best teacher 
will fail. 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 67 

57. General Treatment of a T.esson in Ortlioj;?- 
rapliy. — If all considerations of the meaning and use of 
words, together with their composition, derivation, and other 
grammatical properties be excluded, the only remaining 
objects in view in a spelling lesson are three — pronunciation^ 
syllabication^ and spelling. In preparing and reciting such 
a lesson, the work can conveniently be divided into about 
five distinct stages. 

1 . The pupil should pronounce the words, utider supervision 
and criticism by the teacher.— Th\s is an important exercise, 
and naturally should be the first. When a lesson is assigned, 
a few minutes should be devoted to the correct pronunciation 
of the words composing it. This exercise should be repeated 
just before the words are spelled orally, and at the time of 
recitation. During this exercise the various diacritical 
marks should be observed and commented upon, and any 
important point connected with composition, suffixes, 
prefixes, compounding, etc. will add interest and secure 
attention. 

2. The pupil should study the ivords. — This is a work that 
should generally be done at home, and the teacher should 
insist that it be done thoroughly. If the pupil has a brother 
or a sister, he may easily ascertain when the lesson has 
been mastered. If he can spell for his brother or sister 
every word correctly, he will probably be able to do the 
same for his teacher. The object being to familiarize the 
eye, the ear, and the vocal muscles with the word, no degree 
of thoroughness in this preliminary study is likely to degen- 
erate into a waste of time. 

3. The teacher should pronounce the words and the pupil 
spell them. — ^This is a part of the work that should never be 
omitted, and this is not merely because recitations are impor- 
tant and valuable in themselves, but because omission of 
recitations that have been prepared for quickly leads to 
neglect to make preparation. In giving out the words, 
there should be such an order of procedure as will discourage 
any effort to prepare for the recitation by learning certain 
words that can be predicted as likely to fall to particular 



6S PEDAGOGICS OF ORTHOGRAPHY. § 7 

pupils. Many ways of defeating such dishonesty as this will 
occur to the alert teacher. 

It has already been stated that the pronunciation should 
not indicate the spelling, unless such pronunciation is correct. 
Words should be pronounced by the teacher exactly as in 
correct conversation. Before and after spelling a word the 
pupil should be required to pronounce it — before, to show 
that he understands the word ; after, because the pronuncia- 
tion is a necessary part of the spelling. 

"Trapping," or any other means of deepening the interest 
or awaking a desire to excel, will be found of much help. 
Good results often come from giving a book or some similar 
sign of success in "the Friday spelling match." 

•4. T/w pupils should copy the guards. — This exercise is a 
necessity in familiarizing the eye with word forms. It does 
for this organ what oral spelling does for the ear, and trains 
the muscles of the hand to obey easily and rapidly the behests 
of the mind. This phase of the spelling work is too much 
neglected by teachers, and, while there are decided 
objections against making all the school work in orthography 
consist of written spelling, there can be little doubt that it 
should have at least as much time as oral spelling. 

5. The pupils shojild write the words from die tat ion. — 
After the words of a lesson have been copied from a book or 
from a blackboard, they should be wa-itten at dictation. The 
psychological value of this phase of the spelling work cannot 
be overrated. By means of the exercise the word is made 
familiar to the mind through the organ of sight, and a cer- 
tain musciilar aptitude comes from the act of writing the 
words. The value of this coordination of mental and mus- 
cular action is perhaps not generally recognized. When a 
child first tries to write, he is utterly unable to control the 
movements of his hand, but his conception of the letter 
forms is perfectly definite. The failure in mechanical 
execution is due to the fact that his muscles have not 
acquired the physical habit of acting in obedience to the 
mind. This obedience will become involuntary and purely 
automatic, but to make it so requires much and daily 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 09 

practice. This view is confirmed if we attempt to write with 
the left hand. This is controlled by the opposite hemisphere 
of the brain, to which, for this work, the muscles of the unac- 
customed hand have not yet become subservient. The letter 
forms required are known just as well as before, but the mus- 
cular adaptation and cooperation are wanting". The same 
phenomena are observed when we try for the first time to 
skate, to swim, to play a musical instrument, or to perform 
any physical act to which we are not accustomed. It seems 
clear, therefore, that, in preparing our pupils to use words, 
a condition of easy, and, if possible, automatic correlated 
action should be established between the mind and the 
muscles of speech and of those employed in writing. If the 
student should have any doubt about the necessity for this in 
the case of the muscles concerned in speech, let him .make 
the experiment of reading aloud in German, French, Latin, 
or any other language that he can read silently with ease. 
He will discover a very embarrassing and annoying lack of 
coordination between the mind and the organs of speech. 

58. Effect of AVi'iting- the Same AVord Many Times 
in Succession. — It is an easy inference from the foregoing 
considerations that persistent practice will just as certainly 
establish that which is wrong as it will that which is right. 
If you play a piano exercise incorrectly a few times, especially 
if the performances are in close succession, it is almost 
impossible to get rid of the tendency to repeat the error. A 
chained bear always steps in the same places, and in no 
others, as he takes his exercise around his post. The milk- 
man's horse is with much difficulty prevented from stopping 
at the same places in the same order, morning after morning. 
If we relate an imagined adventure a few times, it comes at 
last to seem to us to be true — a part of our actual experience. 
The French philosopher Thurot says, ' ' Habit is the memory 
of t lie organs. "" Perhaps no better and briefer definition has 
ever been formulated, for the organs do certainly acquire 
an aptitude to do again and again — each time more easily 
— that which they have done before. This very closely 



70 PEDAGOGICS OF ORTHOGRAPHY. § 7 

resembles the reproductive power of memory. This same 
truth, substantially, has been beautifully expressed by 
another writer: " The mind is a spiritual automaton, and 
the body is a material automaton. Like two pieces of clock- 
work, they are so regulated as to mark the same time, but 
the spring that moves the one is not the spring that moves 
the other; yet they go exactly together. " This final com- 
mimity and unison of action is established and perfected only 
by exercising them together. 

All of this has been said for the purpose of making clear the 
extreme harm that results from practices such as the follow- 
ing, very common among teachers: If the pupil misses some 
of the words of his spelling lesson, or is disorderly or dis- 
obedient in any way, and if the teacher deems it necessary 
to detain him after school, he is generally required to "write 
words " as a punishment. The requirement generally is 
that he shall write a limited number of words a great many 
times. Let us suppose that he is directed to write five or 
ten words t^venty or fifty times. The task is always long 
enough to impress him with a sense of the need for haste. 
The work is generally done upon a slate. For the first few 
words the writing is hurried, but yet fairly good. But, as 
the work proceeds, the impression that he must hurry 
strengthens and becomes more imperative, and presently 
he is writing very rapidly, but no expert in writing could 
decipher what he has written. It is surprising how little of 
this kind of work will suffice to negative the most careful 
training in penmanship, and still more surprising is it that 
intelligent and observant teachers do not discover the result- 
ing damage. This and similar devices constitute a favorite 
method by indolent teachers of keeping pupils from the 
mischief that comes from their having nothing to do. 

It may be laid down as a general principle that a teacher 
should carefully watch, and, so far as possible, control in 
pupils the operation of activities that are likely to result in 
the formation of habits; for it is easier to establish and con- 
firm ten good habits than to eradicate one bad one. In 
speaking of habits, Aristotle says, "We should, with all our 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 71 

strength, struggle to the opposite of that to which we are by 
nature the most inclined, as when we row against a current 
or straighten the crooked and deformed limbs of a tree. " 

59. Wvitiiiji' Beautiful or Strikinj»- Passages at 
Dictation. — In addition to writing single words at dicta- 
tion, pupils should be exercised much in copying and writing 
at dictation sentences, paragraphs, and longer poetical and 
prose selections. The reason ior this is obvious. In the 
writing of single words, little or no attention to their mean- 
ing is recpired, but, if entire sentences or longer quotations 
are written, some mental accom])animent is necessitated by 
the thought; and this is a natural preparation for the work 
of original composition, in which propositions must be 
formulated and their connections and relations considered. 
If these excerpts be at the same time instructive and beauti- 
ful, their value is much greater — so much so that many of 
them may be committed to memory. They then become a 
source of mental wealth, and may in later life become an 
inspiration and a guide to action. Many suitable selections 
for this purpose have been made, but the teacher will have 
no difficulty in finding in general literature all of this kind 
of material that he requires. 

The pupils should each be provided with books in whicli 
to copy such selections, and they should be wn-itten with 
extreme care. On Friday afternoons, a delightful exerci.se 
may be had by rec[uiring these to be recited from memory 
by the pupils, and the books should contain nothing that is 
unworthy of such treatment. 

Tliis work may be made more profitable by attending care- 
fully and critically to punctuation, capital letters, paragraph- 
ing, division of words at the end of lines, indentation of 
lines in poetry, and, w'ith advanced classes, to grammatical 
and rhetorical considerations. 

It should be remarked that these selections are likely to 
consist entirely of poetry imless the teacher is careful to 
prevent it. Much of the value that may result will be lost 
unless prose as well as poetry is used. 



72 PEDAGOGICS OF ORTHOGRAPHY. § 7 

60. Siglit or "Flasli" Method in Spelling.— Much 

has been said of late years about the "Flash" method in 
teaching- spelling. The object of the method is to train 
pupils in acquiring a power of instant control of the atten- 
tion, and of concentrating the mind intensely upon one 
object or upon more than one. An experiment that will 
exhibit the differences in this respect among several minds 
is the following: Let several persons walk rapidly past a 
show window, and afterwards let each write the names of 
the different objects he noted, with a brief description of 
each object, its relative position in the window, the number 
of each kind, etc. A comparison of the various results will 
be instructive. Again, if a number of marbles or other 
objects be quickly exhibited and withdrawn, the ability to 
tell their ntmiber and give a description of each is very 
different with different people. Or, if several numbers or 
words, say from four to seven or eight, be pronounced slowly, 
and it be required that they shall be written correctly and 
in order, it will surprise the teacher how various the results 
will be with different pupils. The exercises indicated above 
have been developed into the "Flash" method of teaching 
spelling. Its advocates insist upon its extreme value, and 
some of them would have us abandon every other plan, and 
employ this exclusively. 

The plan has several modifications, their difference being 
that the organ of hearing is addressed at one time, the organ 
of sight at another, and, at still another, both organs are 
operative. To illustrate, the teacher may write upon a 
blackboard one word or several words, erase them quickly, 
and then rec|uire the pupils to write them correctly and in 
the same order. Or, the pupils may be allowed to look for 
one minute at a lesson of, say, twenty words, and then write 
them at dictation. 

In all these exercises, the eyes are the chief agents 
employed in reaching the mind. Similar tasks intended 
for the ears will occur to the thoughtful teacher ; and others 
may be devised in which the eye and ear are both addressed. 

The most obvious objection to the "Flash" method is 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 73 

that impressions made very rapidly upon the mind are gen- 
erally transient. He that would carry in his mind for a long 
time a distinct picture of a face, a landscape, or any other 
object, must see it often, observe it attentively, and note 
carefully the relation of its component elements. It is 
stated that the mind is capable of consciously and distinctly 
perceiving through the eye only about eight separate objects 
in a second. In other words, the element of time is neces- 
sary to sense perception; and it would seem that the depth 
and permanence of a mental impression depend very much 
upon the amount of time expended in acquiring it. 

The writer once knew a teacher that regularly each after- 
noon assigned home work for his pupils, with the under- 
standing that it should be remembered without writing it, 
or indicating it in textbooks. Thus, he would give, exam- 
ples to be divided or multiplied — not more than two or 
three — and words to be incorporated into sentences and 
defined. He urged the value of such exercises in cultivating 
both attention and retention; and doubtless he was correct 
in his theory. 

There is no doubt of the value of the "Flash" method, 
but it is much better to be familiar with all methods and to 
use those best suited to particular cases ; for every situation 
differs in some respect from every other, and each has its 
own requirements. A wise and discriminating eclecticism 
is more to be commended than a slavish adherence to one or 
two methods of procedure. The profession of teaching 
resembles, in many respects, that of medicine. The best 
teacher, like the best physician, avoids the use of nostrums 
and cure-alls, and is expert in adapting the best possible 
treatment to each particular case. 

Gl. Tlie Deflniiig of Words In Connection Witli 

Spellinji:. — Many educators believe that the mere spelling of 
a word is of little con.sequence as compared with its meaning 
and use. In advocating this view, some of them go to the 
extreme of insisting that words should be so thoroughly 
studied that the student shall be able to employ them 



74 PEDAGOGICS OF ORTHOGRAPHY. § T 

afterwards in his ordinary vocabulary. The writer does not 
consider it necessary to discuss this question here, since his 
views as to the two standpoints of discipline and utility in 
the treatment of spelling have already been given. It may 
be remarked, however, in dismissing the subject, that 
extreme theories are nearly always bad theories. 

But, in studying words with the end in view of actually 
using them, the bast means of making our pupils familiar 
with their meaning should be carefully considered. Without 
entering upon the troublesome question of what constitutes 
a correct logical definition, it may be stated that there are 
four practical methods by which a knowle&lge of the meaning 
of words may be acquired : 

1. By giving synonyms and by discriminating among 
them. 

2. By giving antonyms, or oppositcs, or terms of approxi- 
mately opposite meaning. 

3. By the method of '^ particular instance.'" 

4. By formal definition. 

63. Explanation of the Foi*egoingr Methods. — One of 

the most important of these methods is that of synonyms. 
In employing this plan, the teacher should avoid defining a 
word by means of others that are more difficult or in less 
common usj. Thus, if one were seeking a defining synonym 
oi fright e)i, he should prefer scare or alarm to intimidate. 
Since it is extremely difficult to find two words of exactly 
the same meaning — words that may in every case be used 
i iterchangeably — the teacher is constantly required to 
illustrate their differences in sense and use. 

In no department of the treatment of words can better 
helps for the student be found than in this. We have many 
excellent works on " English Synonyms," and some of these 
should be in the possession of every instructor. By their 
constant i:se, he will find much valuable training for him- 
self. His own language will take on greater precision, 
and his thought also. It would be difficult to say which of 
these works is best suited to meet the requirements of the 



§ 7 PEDAGOGICvS OF ORTHOGRAPHY. 75 

teacher, for each one has its own points of excellence. The 
writer ventures to recommend Roget's "Thesaurus of 
English Words," Soule's " Dictionary of English Synonyms, " 
Whately's "English Synonyms Discriminated," Crabbe's 
"English Synonyms Explained," and the latest, but by no 
means the best, James C. Fernald's " English Synonyms, 
Antonyms, and Prepositions." 

This work among synonyms must be carefully graded to 
suit the age and various degrees of intelligence among the 
pupils, and the judgment with which this is done will be a 
comparatively correct measure of the teacher's success. 

The method of defining by opposites is inseparable in 
practice from that by means of synonyms. The two are 
psychologically, as well as practically, associated; for it is 
impossible to conceive of lo/ig except as correlated with 
shorty or of goodness without badness. Indeed, the mental 
effejt produced by the contrast of differences is stronger 
than that derived from resemblances. A child gets a more 
vivid notion of the meaning of hindci' from knowing that it 
is the opposite of Jiclp, than he does from oppose, obstrnet^ 
resist, etc. So that both methods should be used, separately 
and together, as circumstances indicate. 

For conveying a notion of the exact meaning of a term, 
the best possible means is to exhibit the thing denoted by the 
term; next to this is a good picture of it. The objects with 
which we are in daily contact require no verbal definition, 
and any effort to define them in words is worse than time 
wasted. We merely point to a bool', a door, a ivindoiv; in 
the same manner we distinguish colors, shapes, sizes, and 
other attributes; and many actions expressed by verbs, and 
varieties of actions indicated by adverbs, are thus learned. 
In short, anything that can appeal to one or more of the 
senses, either directly or indirectly, by means of pictures, 
gestures, etc., may be represented in our thought with great 
exactness without recourse to synonyms, antonyms, or 
formal definition. ' 

But this is possible with only a small number of the words 
that we are required to use. For other words, an effect 



7(; PEDAGOGICS OF ORTHOGRAPHY. § 7 

approacliing in vividness that derived from the thing itself 
or a picture of it is obtainable by the method known as 
"particular instance." To illustrate, suppose that it is 
desired to convey a precise notion of what is meant by 
delighted. The teacher or a pupil thinks of a situation in 
which no other term will so well express the appropriate 
emotion. ' ' When the little girl found that Santa Glaus 
had brought her a beautiful doll with large black eyes that 
could sleep or wake, she was very much delighted. " 

The inventive power of pupils and their aptness in utili- 
zing their acquired knowledge may be trained by requiring 
them to imagine the situation necessary to illustrate the 
meaning of a word, and to construct a sentence in which the 
word shall occur. This is an exercise that should be in wri- 
ting; otherwise, there is likely to be an undesirable colloqui- 
alism in the sentences. 

Except with advanced pupils, the formal definition has 
little value. There is a certain unavoidable abstractness 
about it that impairs its usefulness in the classroom. Our 
modern teaching puts by far too much stress upon definition 
work. Young pupils should never be asked to meuiorize 
rules., prineiples., or definitions. The pedagogical principle, 
" From the simple to the complex, from the concrete to the 
abstract," requires that pupils should first learn what things 
are. Afterwards, if it be deemed prudent, they may be led 
to evolve a formal definition from the knowledge they have 
acquired. The formulating of a good definition involves a 
high order of classification, abstraction, and generalization. 
The fact is that few people are able to get from a dictionary 
a sharp notion of the meaning of an abstract word. 

63. What Words Say. — Much effort has been made 
to bring within the reach of school children the subject of 
the composition of words. Terms that are made up of Greek 
and Latin roots, prefixes, and suffixes, generally reveal their 
meaning by their Composition. But, to get this meaning 
from them, one must know the exact significance of their 
elements. 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 77 

The following illustrations, one from the Greek and the 
other from the Latin, will make this fact clear to the stu- 
dent : 

Mon, Mono {Monos) = Flex, Fleet {Fh-ctcrc) = 

one, sole. to bend, turn. 

Monareli arclios, ruler. Circxxmflex . . . .circinn, around. 

Monologue. . . logos, a speaking. Flexible iblc, able. 

Monody ode, a song. Reflex re, back. 

Monomania, .mania, madness. Deflect dc, away. 

Monopoly . . . .polcin, to sell. Reflect re, back. 

Monotheism .///^<:'.y, a god. Flexure m-e, ing. 

Monotony . . . .ioiios, a sound. Flexor or, that which. 

The study of words in this way is very interesting- and 
fascinating; for the student is constantly meeting with 
curious instances of words that have wandered far from 
their original meaning-. Indeed, nearly all of our English 
words that are derived from Latin and Greek are mo.saics 
or pictures; and to one acquainted with the languages 
from which they come, a definition is rarely required. 
The words themselves carry in their parts the story of their 
meaning. 

It is doubtful, however, whether a teacher can sticceed 
with this method and material if he does not know Greek 
and Latin. The writer's observation is that teachers and 
pupils manifest but little interest in words studied in this 
manner, unless the teacher has rare art and scholarship. 

G4. Rules of Spellinif . — Rules of spelling have already 
been briefly referred to, and their variety and doubtful value 
have been to some extent considered. But perhaps a few 
rules of widest application may be found useful by tlie 
teacher. The following arc therefore given : 

Rtile I. — Final /", /, or s: Monosyllables ending in f, /, 
or s generally double these finals if they are immediately 
preceded by a single vowel ; as puff, pass, lull, cell, doff, 
miss, etc. 

Some exceptions are if, of, as, lias, was, pus, ks, finis, jws, 
this^ and a few others. 



78 PEDAGOGICS OF ORTHOGRAPHY. § 7 

Rule II. — Other Finals: Words ending in any conso- 
nant other than/", /, or s do not double the final letter; as, 
r//;-, s/i'r, /ur, kin, pan, don, wJiiz, mix, mad, rob, dog, cat, 
cap, mum, etc. 

About a dozen words, with a few proper names, are excep- 
tions to this rule ; as, add, odd, butt, err, inn, egg, bur^rj, ebb, 
purr, fuzz, sirjz, Ann, Kidd, Todd, etc. 

Rule III. — Doubling: Monosyllables and words accented 
on the last syllable, when they end in a single consonant 
preceded by a single vowel, or by a vowel after qu, double 
their final consonant before an additional syllable that begins 
with a vowel; as, rob, robbed ; sin, sinning; abet, abettor, 
abetting; intermit, intermittent ; acquit, acquittal ; repel, 
repelling. 

Exceptions are generally made to this rule if the accent in 
the derivative does not remain upon the root. Thus, we 
have refer and referring, but in reference the accent 
changes and the final consonant is not doubled. So, in like 
manner, we have infei'', inference, infer'ring. 

Final x, being equivalent to ks, is never doubled ; in fact, 
the rule does not apply to words ending in this letter, 
for X is really a double consonant. Thus, box, boxing ; mix, 
mixable, mixed. 

Rule IV. — No Doubling: A final consonant not preceded 
by a single vowel, or when the accent of the word is not on 
the last syllable, is not doubled before an additional syllable ; 
Q.S, fail, failure, failing ; u)ieq7ial, unequal ed ; real, realize, 
realist. 

Exceptions to this rule have in late years been gradu- 
ally disappearing, so that the derivatives of such words 
as sJlovcI, rival, marshal, victual, carol, pencil, cavil, etc., 
are generally preferred without doubling the final con- 
sonant. 

Of course, when a word ending in / takes ly, there are two 
/'s, but this is no exception to the rule; as, really, finally, 
orally, civilly, cruelly, etc. 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 70 

Kiile v.— Final e: Silent c final of a primitive word 
must be dropped before the addition of a suffix beginning 
with a vowel; as, rate, ratable ; true, truism ; debate, de- 
batable. 

Some words ending- in ee ox ge are exceptions; i\s,peaeeable, 
ehaugrable, traeeable, outrageous, aud several others. The e 
is retained in order to preserve the pronunciation of the root. 
This is the reason also for the retention of the e in shoeing, 
and, by analogy, in hoeing. The rule does not apply to 
comp(junds or to prefixes; ^'^, firearms, forearm, vieeagent ; 
final cc, also, is retained ; as, agreeing, fleeing, etc. 

Rule VI. — Final e: Final e of a primitive word is usuallv 
retained before a suffix beg^inning with a consonant ; a,;, state- 
ness, cdgcless, houseless, changeful. 

Some exceptions to this rule are duly, truly, aief'ul, argu- 
ment, judgment, aeknowledgmeiit, abridgment, loholly. 

Rule \"II. — Final J': When final y of a primitive word 
is preceded by a consonant, the y is usually changed into i 
before a suffix not beginning with /; as, merry, merriment : 
cheery, cheerier ; arbitrary, arbitrarily ; pity, pitiful, pitiless. 

This rule applies to derivatives, but not to compounds; 
as, lonely, lonelier ; mercy, merciful, mercy-sister. The follow- 
ing are some of the exceptions: ladyship, babyhood, secretary- 
ship, suretyship. 

Rule A^III. — Final J': When final j' of a primitive word 
is preceded by a vowel, the y is generally retained before 
an additional termination ; as, pays, keys, guyed, chimneys, 
cloying, annoyaiice, joyful. 

The words laid, paid, said, staid {stayed \'^\)XQiQXXQ(S), daily, 
raiment (from arrayment), gaiety, and gaily are exceptions 
to this rule. 

Rule IX. — The Terminations -?^i' AND -ise: The termina- 
tion -izc, when it has the force of to make, to give, or to 
practice, is generally preferable to -ise; in other cases -ise is 
the usual termination; as, rationalize, brutalize, philosophize, 



80 PEDAGOGICvS OF ORTHOGRAPHY. § 7 

phiralizc, canonise, civilise, legalise, organise, apologise ; but, 
1-ise, disguise, enterprise, surprise, supervise, advise. 

The student will notice that -ise is usually a part of a Latin 
root, while -ise is from -iso, an ending of Greek denominative 
verbs — verbs derived from adjectives or nouns, and denoting 
sometimes a state, but more frequently the exercise of agency 
or activity. According to analogy, English denominatives 
of this kind should be spelled with -ise ; as Americanise, 
lionise, centralise. Nearly all words in -ise are mixed 
derivatives. 

Rule X. — Compounds: Compounds usually preserve the 
spelling of their simple components ; as, uphill, peacemaker, 
racetrack, innkeeper. 

One letter is dropped or a hyphen is used if three letters 
of the same kind come together; as, ill- loo king, cJiaffincJi, 
Ross] lire or Ross-shire. 

Some permanent compounds drop an I irowi full, all, and 
fill; as, always, handful, fulfil, withal, careful, sinful. To 
avoid having three s's come together, we have misspell, 
missend, misspend, etc. 

65. Correlations of Spelling-. — There is no subject 
more widely correlated with other subjects than orthography. 
vSince it includes every word in the English language, it may 
be correlated with every subject in the treatment of which 
English is employed. The extreme advocates of correlation 
urge " Robinson Crusoe " as a textbook from which may be 
evolved all other school studies — the physical and mathe- 
matical sciences, history, philosophy, ethics, logic, economics, 
engineering, etc. But why is not the spelling book better 
suited for the purpose than the work of Defoe ? The subject 
that one must know in order to understand all that a given 
word implies, rises easily and naturally from the considera- 
tion of the word itself ; while the way is long and tortuous 
from the situations in "Robinson Crusoe" to the sciences 
supposed to be implied by them. Nothing could be more 
obvious than the transition from the spelling of a term to its 



§7 PEDAGOGICvS OF ORTHOGRAPHY. 81 

meaning and use, and to the sciences in which these are 
exempHfied. But without doubt the student will see how 
iitterly absurd such a scheme of ccjrrelation would be, and 
how slight and vague the results from attempting to unite 
all subjects into a coherent whole consisting of related parts. 
" Spelling for the sake of .spelling" should include nothing 
more than orthography, pronunciation, syllabication, and 
form ; and the study (jf words for practical use should take 
into consideration only such terms as are within easy reach 
of the pupil's intelligence, and are of probable future utilit3\ 
In brief, no subject should be so correlated with others as to 
destroy or weaken the unity of effect that should be sought 
in all rational teaching. In teaching history, for example, 
when we call in the aid of geography, it should be only for 
the purpose of illuminating and emphasizing the subject of 
history. If geography is to be learned, let us study geog- 
raphy; if history, let history engage our undivided attention. 
Correlation work should be incidental and illustrative — 
merely a means to a more important end. "Too many 
irons in the fire at the same time " is as bad for the educa- 
tor as for the blacksmith. The best results in teaching 
are realized when pupils are engaged through a given period 
with not more than three or four subjects. This is deemed 
a wise policy to pursue with the students in our colleges ; 
much more .so is it W'ith the immature minds of children in 
our common schools. But the contrary practice prevails. 
How" often do we meet pupils of the common and the high 
schools, having under their arms great bimdles of books, all 
of which they are attempting to study simultaneously. This 
absurdity is encouraged by the belief on the part of parents 
that the number of books carried by their children is a meas- 
ure of their progress. The pride of parents in their children, 
in the schools, and in the teachers, increases with the number 
of books brought home. 

The writer's advice to teachers would be: Do not attempt 
too many tilings at once ; do tliorouglily ichat yon attempt ; 
avoid confusion and unnecessary correlating; subordinate to 
your main purpose all outside considerations. 



82 PEDAGOGICS OF ORTHOGRAPHY. § 7 

It requires in the teacher a higher degree of skill to instruct 
children in a few subjects than to aiiinsc them with many — 
to master one subject than to get a smattering of a vari- 
ety. But there are education, training, and discipline in 
the one; in the other, only mental dissipation, and undoing 
for genuine study. 



METHODS IN ORTHOGRAPHY. 



APPROVED DEVICES AND ^YORD LISTS. 

66. Classi float ion of Orthographical Worlc. — As has 

already been stated, the object in the study of words is two- 
fold; (1) the attainment of proficiency in mere spelling, 
together with correct pronunciation, syllabication, and 
familiarity with compound forms; (:2) the acquircn':ent of a 
knowledge of the meaning and use of words, including tlieir 
composition and derivation. 

The first of these objects was the only one that received 
serious attention until within the last twenty or thirty years. 
Even pronunciation, syllabication, and form were regarded 
as tmimportant compared with oral spelling. Written spell- 
ing was practiced but little, the ear alone being regarded as 
the only organ required in learning words. But since the 
eye, the muscles concerned in utterance, and those employed 
in writing have become agents necessary to the work, many 
new devices have been tried and found useful. 

The purpose in what follows is to indicate some of the best 
of these in sufficient detail to make them clear to the beginner 
in the work of teaching. 

67. Lists of Words. — It will be necessary to give, in 
illu.strating each device, a few words that are suitable for 
that purpose; but the student must not assume that these 
are in any case sufficient for the actual work of the classroom. 
He should extend them according to the needs of his classes. 
He will find that these lists will grow under his hands, and 



§7 



PEDAGOGICS OF ORTHOGRAPHY. 



83 



that from time to time they should be revised and amended. ■ 
New methods, too, necessitate new lists, different in some 
respect from every other. 

Much labor may be saved, even if some effectiveness is 
lost, by using in class a textbook in spelling, and many of 
these are so excellent that not much can be said against 
substituting them for collections made from them by the 
teacher. Indeed, these books will, in general, be found 
better than selections by the teacher, since not many 
teachers can be entrusted with a work requiring such 
nice judgment and exact appreciation of the needs of his 
pupils. 

In the suggested exercises that follow, no attempt will be 
made to separate those intended for discipline in spelling 
from such as are valuable for other reasons. In fact, it will 
be foimd that many of the words that are required in an 
ordinary vocabulary are of difficult spelling; and it is espe- 
cially important that the orthography of this latter class 
should be made perfectly familiar to the pupil. 

68. Short Woi-ds That Are Often Misspelled.— There 

are many words of this kind that are indispensable in a 
vocabulary. They are doubly useful, therefore, and every 
teacher of spelling should have a collection as complete as 
possible. They should be in exercises in pronunciation, in 
oral and written spelling, and for actual use in sentences. 
A few of them are here given. 



enough 


could 


often 


those 


does 


whose 


again 


which 


always 


should 


there 


done 


once 


they 


any 


many 


what 


their 


where 


been 


hear 


whose 


much 


these 


were 


why 


busy 


here 


sure 


since 


else 


of 


off 


to 


two 



C9. Lessons in Abbreviations. — One of the first things 
that should be taught in connection with orthography is how 
to spell, write, and punctuate abbreviations. In addition to 
this, the pupil should learn to u.se them in speech and wri- 
ting, and to distinguish between those that are admissible 



8J 



PEDAGOGICS OF ORTHOGRAPHY. 



and those that are not. 
important : 



The following; are some of the most 



don't 


they'll 


aren't 


hasn't 


couldn't 


thro' 


etc. 


doesn't 


he'll 


wasn't 


hadn't 


wouldn't 


Mr. 


mayn't 


I'll 


she'll 


didn't 


won't 


e'er 


Mrs. 


we'd 


we'll 


isn't 


weren't 


haven't 


ne'er 


Geo. 


they'd 



After the pnpil has reached a certain stage of progress in 
arithmetic and geography, there should be systematic prac- 
tice in the abbreviations used in those subjects. This is 
something that is rarely done, and yet it is a matter of much 
importance. The abbreviations of denominate numbers 
should be written at dictation, for until this work is under- 
taken in school, uniformity will never be attained. In 
geography, every pupil should know how to write the gen- 
erally accepted abbreviation for the name of each state, and 
for each large city whose name is abbreviated. Advanced 
pupils should be made familiar with such other abbrevia- 
tions as are in very common use; as, /. i\, C.O.D., Dr., Cr., 
ct al., A. Al., LL. D., ibid., A. B., Ph. D., M. D., Hon., etc. 

'70. Words Liiable to Be Mispronoimcetl. — Regular 
exercises in words of this kind should be practiced in every 
school where spelling is taught; yet this is almost entirely 
neglected. Even teachers show by their pronunciation that 
they themselves would be benefited by such exercises. Not 
many persons, perhaps, could be found able to pronounce 
correctly at sight the following words: 



extirpate 


obligatory 


squalor 


vagaries 


arbutus 


legislature 


misconstrue 


bronchitis 


parachute 


docible 


potpourri 


communism 


psalmody 


granary 


anchovy 


rationale 


bouquet 


mauve 


acoustics 


gallows 


equation 


repertory 


coquetry 


acacia 


municipal 


deficit 


isolate 


isothermal 


porpoise 


tortoise 


cortege 


complaisance 


combative 


alias 


admirable 



The teacher should procure lists graduated in difficulty, 
and use them for practice until they have been thoroughly 
mastered. If he is observant, he will be constantly finding 
new words to add to his lists, among which should be many 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 85 

of local peculiarity in pronunciation. This is an exercise that 
will be very beneficial, not only to the pupils, but to the teacher. 
He will get from it much added precision in his own speech. 
It need scarcely be added here that these lists will be 
equally useful for spelling and for other exercises. 

7 1 . Study of Pliouics. — There are two principal methods 
of acquiring a correct and finished articulation. The first 
of these is by the imitation of good models, and the second 
by a systematic study and practice of phonics. There are, 
however, practical difficulties in the employment of either 
method. If all models, all persons whom we hear pronounce 
the words of our language, gave exactly the right sounds of 
the letters, articulated the syllables clearly and distinctly, 
and placed the accent just where it belongs, the first method 
would be an ideal one. For we are by nature imitative. 
Children in a home where English is always elegantly 
spoken, readily acquire the same manner of speech, some- 
what modified, unfortunately, by what they hear from their 
playmates outside. A perfect environment for the cultiva- 
tion of finished speech cannot be found in this or any other 
civilization. People that have been carefully educated and 
trained cannot, or, at least, do not, avoid colloquialisms, 
localisms, crudities of every kind, even slang, in their speech. 
And, when it is remembered that each person is in some 
degree a teacher of many persons, even though undesignedly, 
the extreme difficulty for people in general to acquire finished 
speech will be obvious. 

The principal obstacle in the way of learning correct 
speech from study and practice in phonics is that very few 
teachers are thoroughly acquainted with this subject. Of 
late years, however, much progress has been made, from the 
necessity that teachers have felt of knowing the Phonic 
method of teaching children to read. Even this small 
amount of discipline shows itself afterward in a more accurate 
pronunciation and articulation when children .speak and read. 
But it is only from an extended practice of phonics that the 
best results come. The writer has frequently observed the 



86 PEDAGOGICS OF ORTHOGRAPHY. § 7 

precise utterances of persons that are expert in shorthand wri- 
ting — phonography. With them the sounds^ and not the letters 
that make up words, engage constant attention. They must 
know the correct sound and articulation of words before any 
attempt is made to write them ; and the practice of trying 
their organs of speech upon words is indispensable. In this 
way an instinct for correct pronunciation is formed, just as 
is the case with spelling; and this establishes itself as an 
imperative upon their utterance. 

It would seem to follow, then, that a systematic and per- 
sistent practice in phonics would prove to be a good invest- 
ment in training our children ; but, as is true of nearly every 
other subject, if it is to be made profitable in a high degree, 
the teacher must know it thoroughly, both in theory and in 
practice. If he will procure a good manual on phonics, — 
of such there are many, — and will persist in phonic spelling 
until he is thoroughly master of the subject — until it has 
made its influence felt upon his own speech — he may then 
expect to make it profitable in his classroom work. If the 
writer were asked to advise a teacher concerning this pre- 
paratory work, his advice would be, study phonography — 
shorthand writing by sound — until you can write it cor- 
rectly and rapidly; and to do this, you do not need a teacher. 
You will then be able to teach phonics to your pupils in a 
way that will modify their speech for the better. 

73. The Use of Suffixes in Teaching. — Scarcely any 
teacher of orthography fails to give instruction in the mean- 
ing and use of prefixes in forming derivatives. These are 
nearly all from Latin or Greek, and each usually has an 
exact meaning. This, however, is not so of suffixes in gen- 
eral. They are mostly of Anglo-Saxon origin, and, with a 
derivative, their effect upon the meaning is often difficult of 
statement in words. Hence, suffixes are generally neglected 
in our language work. So important are they, however, 
that the writer gives here the most important of them, 
with their meanings as nearly as possible, together with 
some suggestions as to the best method of using them. 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 87 

73. Alphabetical Arraiigenient of tlie Prlnciiial 
Suffixes. — The numbers preceding the suffixes refer to their 
meaning- as given in Art. 74. 

SUFFIXES. 



1 


ac 


16 


en 


12 


ion 


2 


or 


4 


age 


3 


ence 


20 


ish 


22 


ory 


1 


al 


3 


ency 


19 


ism 


21 


ous 


2 


an 


2 


ent 


2 


ist 


18 


ress 


3 


ance 


2 


er 


2 


ite 


28 


ric 


3 


ancy 


26 


ery 


3 


ity 


24 


s 


2 


ant 


24 


es 


21 


ive 


2 


san 


1 


ar 


18 


ess 


18 


ix 


8 


ship 


1 


ary 


24 


est 


16 


ize 


23 


some 


2 


ast 


24 


eth 


7 


kin 


25 


ster 


5 


ate 


17 


ful 


15 


less 


1 


tial 


6 


ble 


16 


fy 


7 


ling 


3 


ty 


7 


cle 


8 


head 


11 


ly 


3 


ude 


3 


cy 


8 


hood 


12 


ment 


7 


ule 


28 


dom 


2 


ian 


8 


ness 


12 


ure 


27 


ed 


1 


ic 


1 


nic 


13 


ward 


2 


ee 


1 


ile 


7 


ock 


22 


wise 


2 


eer 


9 


ing 


10 


oid 


14 


y 



74. Meaninj? of Suffixes. — There are some exceptions 
to the force of suffixes as given below. It will be necessary, 
therefore, that judgment be used in interpreting their sense 
in derivatives. 

1. Pertaining to; having ; as, maniac, material, momentary, 
stellar, partial, syllabic. 

2. He tliat is, does, makes, or belotigs to ; as, Cuban, complainant, 
scholiast, engineer, assignee, Israelite, artist, grammarian, partisan. 

3. The state of being or doing; as, reliance, privacy, servitude, 
oddity, reference, belligerence, relevancy. 

4. State, or charge ; as, brokerage, nonage, pupilage, storage. 

5. To make, when it forms a verb; as, scintillate, aerate, predicate. 

6. Able, or capable, of being or doing ; as, lovable, legible, stable. 

7. Little, or young ; as, particle, duckling, manikin, lambkin, 
hummock, granule. 

8. Condition, or state of ; as, childhood. Godhead. 

9. Continuiiig ; as, striking, walking. 



88 PEDAGOGICS OF ORTHOGRAPHY. § 7 

10. Resembling ; as, spheroid, anthropoid, typhoid. 

11. Z/Xv, in an adjective; z« « ;//rt;/;/^r, in an adverb ; as, womanly, 
scholarly, slowly, musically, rapidly, only. 

12. Cotidituni, or act of ; as, lodgment, movement, tenure, fusion, 
closure. 

13. Toward; as, forward, westward, windward. 

14. Abounding in ; as, rainy, dewy, smoky, sandy. 

15. Withoitt ; as, moneyless, dreamless, hopeless. 

16. To make ; as, blacken, beautify, legalize. 

17. Full of ; as, beautiful, hopeful, gleeful. 

18. T/ie fetninine of ; as, tigress, lioness, poetess, executrix. 

19. Having reference to a creed, or faith ; as, egotism, altruism, 
deism. 

20. So)neiuhat, or pertaining to; as, greenish, sweetish, Danish. 

21. Having the quality of ; as, evasive, dolorous, glorious, envious. 

22. IVay, or in the manner of ; as, otherwise, edgewise, likewise, 
endwise. 

23. Full of ; as, gladsome, lonesome, burdensome, toilsome, irksome. 

24. With nouns, s and es denote the plural ; with adjectives and 
adverbs, er and est denote degrees ; with verbs, s, est, and eth denote 
the actor. 

25. TJic person, or thing, that ; as, teamster, punster, roadster, 
trickster, malster. In spinster, stcr is a feminine ending. The only 
other Anglo-Saxon feminine ending remaining in English is en in 
vi.xen. 

26. The art of; as, witchery, cautery, cookery, archer}', gunnery. 

27. Did, in a verb ; completed action, in a participle. 

28. Territory of, or office ; as, dukedom, martyrdom, bishopric. 

15, Exercises Witli Suffixes. — Many interesting and 
profitable exercises are possible with suffixes, but of course 
they belong in advanced vv^ork in orthography. In these 
exercises, while spelling is, as always, important, it is the 
meaning of the root and of the suffix, together with the 
special application of the word in actual use, that must 
engage the attention. For, it must be remembered that, 
while the meaning denoted in the etymology of a word 
always contributes to a better understanding of its present 
sense, the two are often widely different. Thus, ambition 
means literally a going around, from avibi and itiis. In 
Rome, 2,000 years ago, an office seeker went around amoj^g 
his voting friends. Today the word denotes merely an 
aspiring after something supposed to be higher and better 



§ 7 PEDAGOGICvS OF ORTHOGRAPHY. 8!) 

than that ah'eady attained. The word admire formerly 
meant to %vo)idcr at, and in this sense it was used by vShake- 
speare and Milton; now it has no such meaning. No hint 
of immortality lingers in cemetery; but, to the ancient 
Greek, Koiiirjri]piov, koimeterion, was a sleeping room, dear and 
diminutive, in which the weary slept, and rested, and ivaked. 
The following will serve to indicate some of the many 
exercises with suffixes: 

1. Form by suffi.xes various derivatives from each of the following 
words, and illustrate their use in sentences: good, return, sly, hope, 
man, etc. . 

3. With each of the following suffixes, form five derivatives, and 
illustrate them in sentences: -en, -oid, -udc, etc. 

;j. In the following derivatives, {a) mention the primitive part and 
the suffix ; {b) give the literal and the present meaning, and account 
for their difference in sense; (<;") illustrate in a sentence the 'present 
meaning of each ; {d) write a brief composition in which shall occur 
the following: nameless, planetary, globule, revolving, stellar, etc. 

4. Mention the derivatives with suffixes in the following, and give 
their meaning: (Here follows a quotation, either prose or poetry.) 

5. By means ()f suffixes, convert the following into diminutives: 
book, braiieh, goose, grain, hill, etc. 

76. Psycliological Use of Rules. — Among the last 
exercises in learning to spell, pupils may be required to state 
or to write rules in exact language — a constructive work 
that makes too severe a demand upon the minds of mere 
children. 

It is an accepted principle in pedagogy that facts should 
precede inductions; examples, rules; processes, principles 
and generalizations; the concrete, the abstract; the .simple, 
the complex. To formulate a rule and cause it to be mem- 
orized, and then to proceed in applying it to particular cases, 
is a reversal of this order. The teacher's aim, therefore, 
should be to develop from many examples a general method 
of procedure — a rule. Whether this rule is merely noted, 
cursorily stated, or expressed briefly and precisely in writing, 
should depend upon the intelligence of the pupils. 

But, while it is not wise to require children to apply rules 
arbitrarily imposed by the teacher, work in spelling should 



90 PEDAGOGICS OF ORTHOGRAPHY. § 7 

not be conducted at random. It is much better to deal with 
words that are classified. These classes may be determined 
by the rules that g-overn their spelling, by the roots they 
contain, by prefixes and suffixes as modifying the meaning 
of roots, by similarity in sound or meaning-, or by any other 
common characteristic. 

77. Exercises With tlie Rules of Spelling?. — The 

statement has already been made that young children should 
not be required to commit rules of spelling to memory or to 
apply them. The teacher may, however, devise many valu- 
able exercises with rules, and yet avoid such requirements. 
The following will indicate how this may be done. He may 
write upon the board or dictate: 

1. Many words ending in e drop this letter before a suffix beginning 
with a vowel ; as, love — loving, lovable, lover, etc. Find ten words 
of which this is true, and write their derivatives. 

2. Write derivatives from the same (or other) ten words, having the 
suffixes begin with consonants. 

3. Some words ending in ce and ge retain the c before a suffix ; as, 
peace— peaceable; strange — strangeness, strangely. Prepare a list of 
five words showing this, and write their derivatives. 

4. Many words ending in a consonant double the consonant before 
a suffix beginning with a vowel; as, rtm— runner, running. Find 
twenty such words, and write their derivations. 

5. Monosyllables ending in a single consonant, preceded by a single 
vowel, double the consonant before a suffix beginning with a vowel ; 
as, strut— strutted, strutting. Write, with their suffixes, ten words 
showing this. 

In this way pupils may be made familiar with the operation 
of all the important rules of spelling, without being required 
to memorize them. 

78. Exercises With Compoiina Words. — It is impor- 
tant that pupils should give careful attention to compound 
words, and should be familiar with the forms in which these 
are usually written, whether they are hyphened, solid, or 
separate. They should learn, too, that a process of change is 
always in operation, and that the approved forms of today 
will many of them be different in ten or twenty years. They 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 91 

should understand the direction of the drift in this matter, 
and know that a condition of permanency is reached only 
when the compound has assumed the solid form. They 
should know that a solid compound may fall apart if it be 
but rarely used. Thus, at first we doubtless had licgf lord 
and licgc man; later, they took the hyphen; then they 
became solid, and now we should write them separately. 
Such things as are gradually introduced, become very gen- 
eral, and then are displaced by something else, often have, 
with respect to their names, a history like this. 

The teacher can place upon the blackboard something like 
the following, have the pupils copy it, and do the required 
work in accordance with the schemes indicated below. 

1. Write as many compounds as you can, and give tlieir approved 
forms ; 

Compounds. Approved Forms. Compounds. .Approved Forms. 

love self-love hat \ hat-box 

self \ \ box 



3. Write the approved forms of the following pairs of words: 
slcain — boat, eye — lash, wheel — barrow, side — light, mi lie — man, 
silk — weed, etc. 

3. Prepare a list of twenty compounds in which a hyphen should 
be used ; and a list of twenty solid compounds. 

4. Write in correct form ten compounds whose second element is 
book, and ten whose first element is fire. 

5. Write and use in sentences ten solid compounds, and ten 
hyphened compounds. 

*T9. Etymological Exercises Involving Spelling. — 

Nearly all spelling books contain many of these exerci.ses, 
usually intended for advanced pupils. Some of our edu- 
cators oppose having pupils do work of this kind, but their 
reasons for the opposition are, many other authorities think, 
not very convincing. As has been said, orthography is gen- 
erally recognized as one of the divisions of grammar, and 
there seems to be no good objection against combining exer- 
cises in etymology with tho.se of spelling, provided always 
that they are not beyond the intelligence of the pupils. 



02 PEDAGOGICvS OF ORTHOGRAPHY. § 7 

Certain is it that much can be done in this way to relieve 
the monotony of routine spelling. 

The teacher will find in some of our latest spelling books 
innumerable exercises of this kind. These should be noted 
by the teacher, and suitable lists and working directions 
prepared. The following exercises will serve to illustrate 
what is intended: 

1. By means of suffixes change the following nouns into adjectives: 
critic, odor. myste7-y, center, home, practice, wind, sphere, story, 
egotism, etc. 

2. Write other nouns containing the ^ame roots as appear in the 
following : sphere, siniplcness, pore, justness, truth, vanity, precision, 
friendship, pallor, requisition, etc. Illustrate in sentences the differ- 
ent ways in which each pair of nouns is used. 

3. Find five nouns {a) that take .f in the plural ; {b) that take es ; 
(r) that change/ into 7/^ J- ; {d) that change/^ into 7V'.f ; (r) that change 
y into ies ; etc. 

4. Write and give the meaning (or use in sentences) of derivatives 
containing the following Latin roots: rupt,fer, cept, viit, le7>, gress, 
dud, din, did, pugn, etc. 

5. Write and define (or use) derivatives from the following Greek 
roots: poly, pod, phi I, phon, thesis, onyin, nod, graph, nion, etc. 

80. Synonyms and Antojiynis. — It would be difficult 
to devise exercises more entitled to a place in the classroom 
than those with words of the same, and words of opposite, 
signification. The teacher is aware, of course, that it is not 
easy to find two terms of exactly the same meaning, which 
may, therefore, always be u.sed interchangeably; and it is 
upon this fact that the peculiar richness of our language and 
its fitness for training the judgment of the pupil depend. A 
great variety of exercises, each with a slightly different 
object in view, may be prepared by the teacher. This 
matter has been treated at considerable length in Pedagogics 
of Grammar, but it is deemed best to make in this place 
some additional suggestions. 

1. Discriminate the following words and illustrate their uses: 
frail, delicate, sickly, unhealthy, diseased, fragile, sick, ill, failing, 
tatsouttd, wasted, worn, emaciated, etc. 

2. Arrange the following verbs as exactly as possible in pairs hav- 
ing opposite meanings: claim, affirm, assert, maintain, assure, assert, 
allege, gainsay, contradict, dispute, deny, waive, retract, disprove. 



§ 7 PEDAGOGICvS OF ORTHOGRAPHY. <)3 

8. Place these words in the order of their strength, beginning with 
the weakest: ^l^id, contented, pleased, rejoiced, elated, jubilant, 
rapturous, triumphant, joyful, happy. 

4. Find the nearest opposites for the following words : symmetry, 
harmofty, diversity, prosperity, analysis, urbanity, rejection, cen- 
sure, bravery, refinement. 

5. In the order of their intensity of meaning, write ten adjectives 
descriptive of the emotion occasioned by failure. Illustrate their use 
in sentences. 

It is scarcely necessary for the writer to say that work like 
the foregoing may be of many degrees of difficulty, and 
suited, therefore, to children in various school grades. But 
this adaptation must be made by the teacher, for no one 
could prepare a textbook for general use. This is perhaps 
the reason why we have so little language work of this kind 
in our schools. 

81. Words Denoting- Collections. — Our language con- 
tains many words, each denoting a collection, but they 
cannot be used interchangeably. Thus, we may say a bevy 
of girls, but not a bciy of ivo?ncn or boys ; a covey of par- 
tridges, but not of geese ; a band of robbers, a drove of horses, 
a Jioek of birds, etc. In learning our language one of the 
chief difficulties experienced by a foreigner lies in the neces- 
sity for discriminating words of this kind ; and what is true 
in the case of foreigners is true also in that of our own 
children. Both are equally beginners, and what must be 
done for the one should be done for the other. In our 
schools, no special training in these matters seems to be 
regarded as important. Whatever there is of it is accidental, 
and it is just this purposeless work, this absence of prevision, 
that detracts so much from the value of a teacher's work. 
Let it be determined in advance what is important to be 
learned and why, and let relative or comparative values be 
fixed as nearly as possible, and then let each matter be incor- 
porated as a distinct part of a general scheme of work. This 
is something that cannot safely be trusted even to the best 
memory. No teacher should expect that necessary things 
will be suggested to the teacher at the right time and place. 



94 PEDAGOGICS OF ORTHOGRAPHY. § 7 

They may or they may not occur to him when they should; 
hence, the value of note books. These books, collectively, 
should speedily constitute a source from which may be drawn 
the material, the devices, and the methods of procedure that 
are indispensable in organizing the work of a coming term. 

The teacher will be surprised to learn that there are in 
common use more than two hundred words of the kind 
referred to above — words denoting collections. The follow- 
ing suggested exercises will be found useful in practice : 

t. Prepare a list of words that denote collections, and make the 
list as nearly complete as possible. 

2. Write twenty of the words in (1) that are in commonest use, and 
modify each by a prepositional phrase ; as, a pool of maftufacttirers, 
a gala.xy of beauties. 

3. Find the collective nouns that may be modified by each of the 
following phrases: of robbers, of bees, of cattle, of dishes, of minerals, 
of plants, etc. 

4. Write the following collective nouns, each with one or more 
appropriate modifying phrases: presbytery, synod, council, cotigress, 
squad, squadro7i, series, colony, den, legation, knot, succession, syndi- 
cate, universe, school, wilderness, battery, catalogue, etc. 

5. Find from a dictionary the derivation and the literal meaning of 
the following collective nouns: synod, canopy, gala.xy, presbytery, 
horde, universe, collection, aggregation, succession, constellation, 
niultititde, catalogue, complement, etc. 

82. Words Expressing Diffei*ent Aspects of tlie 
Same Idea. — All our writers on synonyms arrange words in 
accordance with some leading ideas. These ideas may have 
relation to physical qualities as perceived by the senses, or 
to metaphysical qualities as conceived by the mind. Most 
words having metaphysical or ideal applications were origi- 
nally employed in a physical sense, and it is a knowledge of 
this sensible use that gives vividness to words when they are 
transferred to ideal uses. Thus, a linguist sees a needle in 
ac2itc, ahorse in cavalier, a ladder m scale, clunbinginascoid, 
a flock in pecuniary, or gregarious; and st in stajid, station, 
steady, stake, status, substantive, etc. tells him the story of 
erectness and fixity ; hence, the importance to the student of 
finding the root or original physical sense of words, especially 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 95 

of such as have strayed entirely away from that meaning. 
Indeed, without knowing- the etymology of words, it is 
impossible to use them with perfect discrimination. 

The pupil, in order to acquire this knowledge, must have 
access to a standard dictionary, and inust know how to use 
it; and, therefore, the exercises suggested below can be 
undertaken with profit only by advanced pupils. 

1. Find, and illustrate the use of, ten verbs implying motion down- 
'■a'tird; also, ten implying vioiion upward. 

2. Write all the words you can that implj' increase in physical 
volume; in physical area ; in physical length. Select from your lists 
those words that have ideal ai^plication, and illustrate their use. 

3. Find ten verbs implying use of the sense of sight. Explain and 
illustrate their difference in meaning. 

4. Referring to (3), give all the related nouns, adjectives, and par- 
ticiples. Thus, verb, view; uoim, view, vision; tuljeetivo, 
visible, viewable; particii>lo, viewing. 

5. Make lists of the verljs, the nouns, and the adjectives employed 
with reference to motion from a place; with reference to motion 
toward a place. Explain their difference in meaning. 

83. Words Belonging to a Given Environment. — 

A valuable and much used exercise with words consists in 
requiring the pupil to write correctly lists of words belong- 
ing to particular situations. Thus, the field, the garden, the 
kitchen, the parlor, the farm, the city, the ship, and the 
railroad each has a great many objects, actions, qualities, 
processes, and products that belong there. vSome of the 
terms denoting these things are of difficult orthography, and 
all are useful in an ordinary vocabulary. It should be 
remarked that exercises of this kind deal mostly with nouns, 
and are therefore suitable for the work of young children. 
In giving a notion of the meaning of nouns, children may be 
required to indicate any, or all, of the following: 

1. Its physical qualities; including shape, size, material, 
color, smell, etc. 

2. Its origin. Did it grow, or was it made by man ? 
Etc. 

3. Its use or function. This last is perhaps the most 
important basis of classification, and the one most commonly 



96 PEDAGOGICS OF ORTHOGRAPHY. § 7 

employed. Of course, many exercises of this kind with 
other parts of speech are possible. Some of these are : 

1. Write the names of animals that are useful to man, and state in 
what respect they are useful. 

3. Mention some common wild flowers ; also, some grown for orna- 
ment. 

3. Give the names of useful plants and trees ; also, the names of 
the fruits and vegetables, domestic and foi-eign, that you would expect 
to see in a large market in New York City. 

4. Write (a) the names that are difficult to spell of parts of the 
human body; (/^) the words that denote what the mind can do. 

5. Give the names {a) of ten _/is/i; (/') of ten trades or professions; 
(c) of ten tools; (li) of ten terms used in miisie; (e) of ten birds; {/) of 
ten inetats; {g) of ten precious stones; (//) of ten games; (z) of ten 
terms used in geography. 

84. Spelling- From. Pictures. — Closely related to the 
exercises indicated above is that of spelling- from pictures. 
In both cases the reality is absent, and the pupil is required 
to find a substitute for it — in the first, a mental picture, and 
in the second, a physical representation. The mental picture 
cannot be reproduced for reference by the teacher and the 
class in criticizing the pupil's work, while the physical 
picture is more convenient for this purpose than even the 
reality. In this fact lies the opportunity of introducing 
verbs, adjectives, adverbs, and other parts of speech besides 
nouns. Pictures suggest and represent things and their 
qualities; they suggest actions in various degrees, and rela- 
tions that require prepositions and conjunctions. With the 
picture before him, the pupil may be asked to explain in 
what he found a suggestion of particular words in "his list. 

It should be added here that with young children no better 
subject for a composition can be found than that furnished 
by a good picture. From the requirement that a pupil shall 
tell merely what he sees in the picture, this exercise may 
rise in difficulty into an account of the differences and like- 
nesses of qualities in the objects depicted, the actions sug-- 
gested and their purpose, the manners and degrees of the 
action, the cause, purpose, and result of the conjunction of 
olijccts and actions in the picture; and with all these may 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 97 

enter relations of time and place. In short, the pupils mi 
write, as if from their own experience, a composition cover- 
ing the things shown by the picture or suggested by it. 

Many teachers require their pupils to indicate by a picture 
of their own making, at the top of the paper, with or without 
marginal pictures, the main points or incidents related in the 
composition. Thus, if a pupil is writing about the polar 
bear, some very striking pictures may be made showing the 
animal in his habitat and in characteristic action. It is urged 
as a reason for this practice that the inventive power of the 
mind is increased by means of the picture — a claim about the 
truth of which there can be no doubt. Even the mature 
reader gets a very much more realistic and vivid impression 
from an illustrated book than from the text alone. How much 
our interest in the " Pickwick Papers" would be lessened if 
the pictures of the inimitable philosopher were missing. 

85. Exercises Witli Prepositions. — To be able to choose 
m every case the appropriate preposition, is by no means a 
simple matter, and it should be persistently and carefully 
taught. The subject, however, receives but little attention, 
generally none at all, in our schools. Although no question 
ot pronunciation or spelling is involved, the very vital rela- 
tion of the preposition in our vocabulary gives this part of 
speech peculiar interest and importance in language teach- 
ing. No excuse need be offered, therefore, for introducing 
the subject at this point. 

The c[uestion as to what preposition should be used with a 
particular word is determined in general by one or more of 
tnree circumstances. 

1. By tJic prefix of the uKird; as, advert to, inscribe upon, 
etc. Here the first prefix means to and the second on or upon. 
Hence, the English prepositions are determined by the mean- 
ing of the Latin prefixes. 

2. By the meaning of t/ie word ; as, patient in or amid 
misfortunes; reason of ox against a principle or theory, j^>r 
an action ; disappointed at a failure, in love, of what was 
expected. 



98 PEDAGOGICS OF ORTHOGRAPHY. § 7 

3. By common 7isagc; as, confide to one's care, in one's 
word or honor ; two persons may have confidences zuith each 
other, or there may be confidences among several persons ; 
preserve in alcohol, xvith care, for my son, by vigilance, from 
danger, against future need. 

In the exercises necessary for the proper development of 
this subject, the teacher may : 

(1) Supply the pupils with words each of which takes one 
certain preposition, and he may require them to indicate the 
preposition and illustrate its use. 

(2) Supply certain prepositions, and the pupils may use 
each in sentences with other suitable words. 

(3) Supply sentences with blanks indicating missing prepo- 
sitions, and require the pupils to fill the blanks. 

(4) Require the pupils to use a specified word with several 
diiferent prepositions, illustrating each in sentences. 

It must not be forgotten that this is a work intended not 
so much for discipline as for practical use ; hence, the exer- 
cises should be confined to the probable future vocabulaiies 
of the pupils. No time should be expended upon combina- 
tions that are rarely met or used. 

86. Form and Matter of IJetters. — If there is a subject 
with which orthography is more closely correlated in practice 
than it is with any other, that subject is letter writing. One 
of the most frequent and important applications of the knowl- 
edge gained from a study of orthography is to correspondence. 
Nearly everything connected with this subject has relation to 
orthography. Of our latest textbooks on spelling, almost all 
contain exercises in letter writing. vSome of the expedients 
employed are for the teacher. 

(1) To supply brief letters showing the approved forms, 
positions, punctuation, etc. of the various parts. These are 
to be copied by the pupils with the object of making the 
mechanical construction and arrangement of letter elements 
familiar to them. 

(2) To dictate to the pupils brief letters, and require them 
to be written correctl}'. 



§ 7 PEDAGOGICvS OF ORTHOGRAPHY. 99 

(o) To furnish in outline the data of letters, and have the 
pupils write them in full. 

(4) To require pupils to write various kinds of letters to 
imaginary correspondents. 

In this work, spelling- is to be attended to closely, but even 
more important are pronunciation, capitalization, division of 
words at the end of lines, parag-raphing, and general correct- 
ness of form. 

87. Pedagogical Objections to Correlative Work 
Ijike the Foregoing-. — The writer is aware, of course, that 
in many quarters there is much opposition to the inclusion in 
orthography of anything more than spelling, pronunciation, 
and syllabication. A late spelling book contains the follow- 
ing in its preface : 

"Grammars, rhetorics, geographies, histories, and even systematic 
works on composition, are useful — and so are spelling books. But it 
does not follow that they should all be combined in one. It is possible 
to drive a nail with a chisel ; but nails can be driven better and quicker 
[more quickly] with a hammei\ So a textbook is better for a special 
use by being specially adapted to that use. 

"These facts will account for the absence from this work of many 
puzzling exercises in the construction of sentences, and in fitting words 
to parts of ready-made sentences, as well as for the lack of lessons and 
examinations in geographj', grammar, and history, with which some of 
the modern spelling books abound. It is believed to be better at times 
to concentrate the attention of the student upon spelling; and, accord- 
ingly, that all matter tending to distract his attention from the special 
work of learning to spell should be excluded from the spelling book." 

88. Remarks I"i)on Tliese Objections. — It may be 

remarked that the author of the foregoing criticism on the 
correlation of spelling is head master of a normal school 
where provision is made for the systematic study, in its 
proper place, of everything required to prepare students 
thoroughly for aij intelligent comprehension and discharge 
of the duties that await them. But this is not the usual case 
in the schools where spelling is taught. In most schools, the 
student will in all probability never hear in the classroom 
anything on the subject of letter writing, unless the teacher 



100 PEDAGOGICv^ OF ORTHOGRAPHY. § 7 

introduces it in correlation with something else. When he 
studies geography, he will give no attention to the spelling 
and pronunciation of geographical terms. Of punctuation, 
too, he is likely to hear nothing. Indeed, nearly every teacher 
is, from his own experience, aware of the truth of these 
statements. 

The writers on hygiene tell us that a variety of physical 
food is necessary to health, and that the assimilation and 
appropriation of its useful elements are better and easier if 
these eleinents are varied in character. We all know how 
weary one becomes of a diet consisting exclusively of oat- 
meal, eggs, or meat. Something like this is true of the 
mind. If a pupil is compelled to concentrate his attention 
exclusively i:pon one subject, he makes less rapid progress 
in it than if his time is judiciously divided among several 
subjects. Even a philosopher finds rest and relief from his 
abstruse specialty by resorting at times to the newspaper or 
the novel. 

Knowing that certain indispensable things are not dis- 
tinctly provided for in the course of study that he follows, 
the thoughtful teacher will consider how, and in connection 
with what subject, he can supply the omission. He is 
convinced that eveiy person should know how to write a 
creditable letter, and that ignorance in this will be the 
occasion of much futvire embarrassment and even pecuniary 
loss. He sees to it, therefore, that at the right time and 
place the want of prevision on the part of those that arranged 
the course of study shall cause his pupils the least possible 
disadvantage. He realizes that he is " confronted not by a 
theory but by a condition. " 

Yet, whatever work of this kind may be necessary, the 
teacher must never lose sight of the main subject in hand. 
Its unity must remain and be exemplified in his work. 

89. Correlation of Spelling With General Informa- 
tion. — There are many matters of general information that 
are often overlooked in elementary education — and this is 
all the education received by 95 per cent, of American 



§ 7 PEDAGOGICS OF ORTHOGRAPHY. 101 

children. These matters are not merely ornamental — they 
are extremely useful and important. The man or woman that 
knows nothing of the great men, inventions, discoveries, 
epochs, battles, and creeds of the world is badly handicapped 
as a member of society, and he can learn about them only 
incidentally. No school will teach him anything worth 
speaking of about these matters. We must rely upon our 
teachers to supply data that are indispensable to a wide 
mental horizon — to large views of men and things,, the world 
and its contents. 

Many of our spelling books suggest lines of w^ork of this 
kind — work that meets in the best possible way the cravings 
of the mind to know, of the imagination to create, and of the 
fancy in its aerial play. This is not a diversion of time from 
a more important subject ; it is a legitimate and necessary 
attempt to provide for a real want of the mind. Some of 
these exercises are indicated in briefest outline below, but 
besides these there are many others of equal importance. 

1. Learn to spell the following names of authoi-s ; find out what you 
can about each: Dickens, Thackeray, Macaulay, etc. 

2. Who were the following named persons; when did each live; 
for what was each celebrated ? Croesus, Theseus, Hercules, Lycurgus, 
Aristides, Demosthenes, etc. 

8. Who wrote the following ? Tell something of each work : "Pick- 
wick Papers," "The Caxtons," " Romola," etc. 

4. Find out and write correctly the names of the " Seven Sages of 
Greece." Tell something about each of them. What were the " Seven 
Wonders of the World ?" 

5. What cities are known as follows ? " The Hub," " The Crescent 
City," "The City of Churches," "The City of Magnificent Distances," 
"The Electric City," etc. 

6. Write the names of each of the United States, and give, as far as 
you can, their popular names. 

7. Write twenty geographical names of South America that you 
consider of difficult spelling or pronunciation. 

8. When and by whom were the following inventions made ? Cot- 
ton-gin, telegraph, kinetoscope, steamboat, gunpowder, printing, 
mainner's compass, telescope, etc. 

9. Write the names of ten characters in Greek mythology. Tell 
something of each. Also, ten of Roman and ten of Scandinavian 
mythology. 



102 



PEDAGOGICS OF ORTHOGRAPHY. 



§7 



10. Give the names of ten of the world's greatest military leaders, 
and tell something interesting about each. 

How much besides the spelling and pronunciation of the 
names involved above should be required will depend upon 
the circumstances in each case, and, of these, no one can 
better judge than the teacher. That much of this kind of 
work should have a place in the classroom seems to the 
writer indisputable. 



90. Test Words for Spelling;. — Most works in orthog- 
raphy contain lists of words for test spelling. In these lists 
will nearly always be found terms that are never employed 
even in learned conversation. vStich words have no other 
claim to attention than that their spelling is difficult; but, 
since we have an abundance of useful words of irregular 
spelling, it is well to use as many of them as possible. For 
examinations in spelling, however, difficult words, without 
regard to their usefulness, are nearly always chosen. 

The following will indicate in general the writer's notion 
of the kind of words selected as tests for teachers that are 
required to undergo examinations in orthography. The 
teacher can extend it as his needs require. Of course, only 
advanced pupils should practice such words. Similar col- 
lections graded to suit should be prepared for each year of a 
pitpil's school life. 



whippoorwill 

cemetery 

alpaca 

cochineal 

caterpillar 

calendar 

paroxysm 

separate 

operate 

opportunity 

suppurate 

crystallize 

flageolet 

parricide 

bronchial 



sedative 

psychology 

catastrophe 

hyacinth 

pyrotechnic 

raspberry 

pentateuch 

hydraulics 

pennyroyal 

patriarch 

decalogue 

corollary 

syllogism 

Pharisaic 

caisson 



philanthropy 

altruism 

accouter 

acerbity 

saccharine 

foliaceous 

calking 

gauger 

giaour 

philippic 

phylactery 

philology 

etymology 

antonym 

pseudonym 



shillalah 

barytone 

alinement 

anachronism 

plagiarism 

garlicky 

redeemable 

dentifrice 

plaguy 

sergeant 

chalybeate 

vicinage 

pimpernel 

immaculate 

pleurisy 



PEDAGOGICS OF ORTHOGRAPHY. 



103 



taciturn 

rarefy 

necessary 

abatable 

hysterics 

asphyxiate 

daffodil 

cabalistic 

dactylic 

czarevitch 

apologize 

mustache 

bandanna 

whinneying 

dagueri-eotype 

scintillate 

anonymous 

quinsy 

mignonette 

caviling 

flagitious 

facetious 

acquiescence 

catalepsy 

casuistry 

centennial 

annually 

elixir 

cauterize 

damageable 

aberration 

chirurgeon 

caricature 

erysipelas 

basilisk 

mahogany 

macerate 

dilemma 

pistachif) 

maintenance 

sibylline 

appendicitis 

apostasy 

cymbals 

symbols 



sedentary 

monotony 

supersede 

procedure 

precedent 

accelerate 

hybridizing 

proceeding 

deceiving 

believing 

ichneumon 

persimmon 

banana 

lachrymose 

pharyngeal 

emissary 

shampooing 

calcareous 

emollient 

kerosene 

em^iyrean 

empiricist 

attrition 

gazetteer 

poignancy 

lascivious 

chrysalis 

diapason 

synthesis 

antipathy 

delirious 

isosceles 

nominative 

pyramidal 

hypotenuse 

melodeon 

labyrinth 

parliament 

sovereign 

esophagus 

bronchitis 

aqueduct 

contiguity 

colonel 

soliloquy 



gelatin 

boudoir 

piecemeal 

barbecue 

chameleon 

truncheon 

incensed 

cephalic 

reconnoiter 

reconnaissance 

sycophancy 

judgment 

syllabication 

bourgeois 

fricassee 

demoniacal 

cerulean 

trysting 

jaundice 

landau 

jinrikisha 

obscenity 

amphitheater 

anagram 

piquancy 

diaphragm 

macaroni 

incai'cerate 

cicatrice 

sinecure 

auspicious 

seditious 

irascible 

implacable 

diphtheria 

rutabaga 

rhythm 

indelible 

stratagem 

anathema 

malfeasance 

chimerical 

ribaldry 

meerschaum 

lieutenant 



peritonitis 

ephemeral 

transient 

jeopardize 

incomparable 

symbolize 

syzygy 

surplice 

symmetry 

allopathy 

hydropathy 

homeopathy 

caoutchouc 

chibouk 

brochure 

anthracite 

capacitate 

desiccation 

pneumatics 

mnemonics 

refragable 

synagogue 

gossamer 

britannia 

tumefaction 

buccaneer 

metallurgy 

desuetude 

innocuous 

chiropodist 

knicknack 

susceptible 

synecdoche 

nonpareil 

diaphanous 

omniscient 

macaroon 

ligneous 

catarrh 

diarrhea 

asthma 

pneumonia 

sciatica 

rhetoric 

sycophant 



iUi 



PEDAGOGICS OF ORTHOGRAPHY 



^7 



capillaries 

auricle 

Eustachian 

hymeneal 

rebellion 

incredible 

hickory 

cynosure 

sassafras 

sycamore 

patella 

jessamine 

fuchsia 

alyssum 

amaryllis 

iguana 

succotash 

quintessence 

emanation 

transcendent 

garrulous 

cadaverous 

kaleidoscope 



criticism 

tantalize 

titillate 

appellant 

subjjoena 

propeller 

boatswain 

azalea 

asparagus 

ageratum 

sieve 

anemone 

acacia 

callisthenics 

acrobatics 

centipede 

cyclopedia 

accordion 

cauliflower 

aureola 

aeronaut 

ventriloquist 

deference 



taciturnity 

gayety 

luncheon 

acquiescent 

glycerin 

ipecacuanha 

annatto 

rhomboid 

finical 

chancellor 

belladonna 

bergamot 

broccoli 

bouvardia 

ealadium 

columbine 

plaguing 

cannibal 

obsequies 

auscultation 

chalcedony 

sardonyx 

sarcophagus 



acoustics 

satellites 

laryngeal 

comparable 

insidious 

lettuce 

lineament 

excellence 

achievement 

bereavement 

bouquet 

tmesis 

metonymy 

simile 

metaphor 

allegory 

honeysuckle 

chrysanthemum 

chinkapin 

purslane 

jjheasant 

portulaca 

licorice 



A SERIES 



OF 



QUESTIONS AND EXAMPLES 

Relating to the vSubjkcts 
Treated of in this Volume. 



It will be noticed that the various Question Papers that 
follow have been given the same section numbers as the 
Instruction Papers to which they refer. No attempt should 
be made to answer any of the questions or to solve any of 
the examples until the Instruction Paper, having the same 
section number as the Question Paper in which the questions 
or examples occur, has been carefully studied. 



PEDAGOGICS OF ARITHMETIC. 

(PART 1.) 



(1) Explain what is meant by automatism in arithmetic, 
and describe the inost eifective means of attaining it. 

(2) Give two examples of arithmetical drill exercises that 
have no obvious purpose, and two others, each of which has 
a very definite object. State the object of each of the latter 
pair. 

(3) Give a general account of the concrete appliances 
that should be used in the first work in arithmetic. 

(4-) Give in your own words the substance of the para- 
graph on the grammar of arithmetical language. Give Dr. 
Bain's general principle, and illustrate it by an example. 

(5) Describe and illustrate the exercise called "Telling 
Stories in Arithmetic." In what respects does the child 
receive profit from these stories ? 

(G) Write the formulas given in Art. 21, and make an 
easy example in fractions illustrating each. 

(7) Explain some of the advantages to be gained by the 
use of type formulas. 

(8) Make an example illustrating each transposed form 
of the equation ;// = cd—ab^ as explained in Art. 33. 

§1 



2 PEDAGOGICS OF ARITHMETIC. § 1 

(9) Describe the various drills that are useful in teaching 
addition. 

(10) Make a drawing of the "General Scheme" of drill 
work in subtraction, and show the blackboard form that you 
woulxl use when 8 is the subtrahend. 

(11) Show the form for blackboard drill in teaching 
multiplication by 9, with carrying. 

(12) Show by a drawing the "General Scheme" for divi- 
sion drill. 

(13) Give in your own language the substance of what is 
contained in Art. 37 on the perception of number. Explain 
its application to pedagogics. 

(14) Explain the common method and the scientific 
method of teaching notation. 

(15) Describe fully and illustrate the use of and \n read- 
ing numbers. Give cases that would be ambiguous without 
the help of the distinction in question. 

(16) Give a concise sketch of the earliest work in frac- 
tions, as outlined in Art. 50. 

(17) Subtract of from 7^ in the manner explained in 
Art. 53 (13), and write in full the explanation of each step. 

(18) Describe the best method of subtracting 4| from 9|. 

(19) What should children be required to say in multiply- 
ing orally ^ by T ? 5f by 8 ? 7f by 5 ? 

(20) Show, by dividing such a figure as a circle, square, 
or line, that f of f is \. 

(21) Write ten examples suitable for " t'?*?/'/*'/ ]]\)?-k'' in 
connection with the study of "The Number 5" (Art. G7). 

(22) In connection with the study of "The Number 0" 
(Art. 68), prepare ten good questions for use under the 
head of "The Applied Number." 



§ 1 PEDAGOGICS OF ARITHMETIC. 3 

{2o) Write for "The Number 7 " suitable work under the 
head, "The Subdivided Unit." 

(24) Write the matter for measuring with 3 and with 4 in 
connection with the study of " The Number 9." 

(25) Write in full, suitable matter for the woi-k included 
under all the heads in connection with the study of " The 
Number 7." In doing so, follow the plan given in the 
Instruction Paper. 



(2G) If a drill form like the accompany- 
ing were placed on a blackboard for oral 
work, what analysis of each should be | of 
required of the piipils ? Write the analysis 
in full. 



8 



= ? 



(27) Give the best analysis that you can for the following 
example: If f of a number is 12, what is | of the number ? 

(2.S) By means of a diagram find the sum of i and i. 

(20) vSht)w by a diagram the several successive steps in 
the analysis of the following example: If | of a certain num- 
ber is 15, what is 4 of the number ? Make your diagram as 
neatly as possible. 

(30) Show very neatly five good blackboard forms for 
drill work in fractions, and write out in full the proper oral 
statement that you would require the pupils to give for each 
drill. These drills should be of your own devising. 



PEDAGOGICS OF ARITHMETIC. 

(PART 2.) 



(1) As in Art. 3, use the following example and show 
what form the minuend will take in order to explain the 
carrying necessary in the following example : From 
10,011,010 take -4,875,927. 

(2) Use the example 8,012,805-5,871,698, and write a 
full explanation of the method of subtracting by addition. 

(3) Explain and illustrate the method of subtracting the sum 
of several numbers from one number by the method of adding. 

(4) Write ten multipliers of special form similar to those 
given in Art. 11, and explain what is special in each. 

(5) By the method explained in Art. 13 perform the 
following operations, and show the diagram for each : 
{a) 05X37; {h) 123x450; (r) 3, 004x532; {d) 4,507x23; 
(^•) 824X3,502. r [ci) 2,405. 

\b) 50,08§. 
Ans. .j (r) 1,030,048. 
j \d) 105,041. 
t 0') 2,935,088. 
(0) By the method explained in Art. 14 find the value 
of the following: (^?) 3,214x998; {b) 59, (i48 X 9,997 ; 
(r) 3,420X1,000; {ci) 8,697x992; ^c) 9,999x10,004. 

{ {a) 3,207,572. 
I \li) 590,301,056. 
Ans. -! [c) 3,44(5,556. 
\d) 8,627,424. 
. {c) 100,029,996. 



2 PEDAGOGICS OF ARITHMETIC. § 2 

(T) Perform each of the following divisions by the best 
method: («) 736,284-=- 98; (^) 3,692,847^ 007; (^ 43,2(;4,795 
^1,002; {d) 386,400,101-1-9,992; {c) 730,401, 061 h- 10,008. 

I (.0 7,ol3if. 



{l^) 



9 7- 



Ans. -I (0 43, 178^^2 • 
I {d) 38,670|Mi 
I 0) 72,981t-VVoV 

(8) Solve the following by the method explained in Art. 
22'. {a) 842,376 -^ 123; {b) 5,964,872 h- 7S9; {c) 1,230,256 
-r- 204; (fl') 987,024,673 -^ 27,042. \ [a] 6,848iV%. 

A^, ! (^') ^560/i- 
'^"'- ■] (.) 6,030iff. 

[{d) 36,499ifi.i|. 

(9) Give with illustrations the principles relating to the 
divisibility of numbers by 2, 3, 4, 5, 6, 8, 9. 

(10) Explain how you would ascertain without referring 
to the table whether 937 and 1,747 are prime numbers. Give 
for each number the list of divisors that you would try. 

(11) Show the operation of separating 59,400 into its 
prime factors. 

(12) By the abbreviated method explained in Art. 35, 
find the G, C. D. of the following: {a) of 11,407 and 22,631 ; 
{b) of 13,221 and 27,685; {c) of 16,147, 208,947, and 
329,929. r (a) 61. 

Ans. j (/;) 113. 
I (0 241. 

(13) Find the value of the following, and arrange your 
work as suggested in Art. 39: {a) f +f + }§ + 11+ H; 
(/,) 44-|-8f + 7H + 13t + 16f. 

AnsM-) ^tV 
I {b) 50ifi. 



§ 3 PEDAGOGICvS OF ARITHMETIC. 3 

(14) As directed in Art. 41, perform the followino^ opera- 
tions, clearly indicating or explaining each step : (a) :)2| X (Jl|- ; 
(/;) 1231X4(351; {c) 41i->|X(;34. {(a) 2,023if 

Ans. ; (/;) 57,509|. 
[{c) 31,429if. 

(15) Explain fully, and illustrate the precedence of signs. 

(IG) Make as clear as possible the reason for inverting 
the divisor in dividing one fraction by another. 

(IT) To what single discount is each of the following 
series equivalent: (a) 30^, 40^, 20^, and 10^ ? (/;) 30^, 20^, 
10^, and bi ? (r) GO^ 60^, and 40^ ? | {a) 09.76^. 

Ans. \ \h) 52.12^. 
L(6-) 90.4^. 

(18) By means of the formiila, / = , find in what 

time, at G^, 1800 will yield *110.40 interest. 

Ans. 2 yr. 3 mo. 18 da. 

(19) Find the exact interest at m of $4, GOO from Jan. 20, 
1900, to July 30, 1900. Ans. 1108.32. 

(20) By the sixty-day method find the interest of *8,300 
at G^ for 238 days. Ans. 1329.23. 

(21) What is the difference between the true discount and 
the bank discount of an obligation for $75,000 discounted 
45 days before its legal maturity at 6^ ? Ans. $4.19. 

(22) By the method of equal factors find the cube root of 
226, correct to five decimal places. Ans. G. 09119. 

(23) By using the formulas in Art. 97, {a) find (^ when 
V = 1,000; (/;) find Fwhen C = 12. 

Ans -^ ^''> ^^•^•'• 
■ \ (/;) 29.18. 

(24) By the methods explained in Art. 100, find five sets 
of numbers that may exactly represent the three sides of a 
right-angled triangle, and prove that they are correct. 

(25) By nsing the formula given in Art. 101, find the sum 
of all the odd numbers less than 100. Ans. 2, 500. 



PEDAGOGICS OF GRAMMAR. 

(PART 1.) 



(1) In what two respects can a person be benefited by the 
study of English grammar ? 

(2) .What is meant by inflected as applied to language ? 

(3) What are the four usual divisions of grammar ? 

(4) Why should the first of the four divisions be excluded 
from textbooks on English grammar ? 

(5) Why should the subject of Punctuation be treated in 
a work on English grammar ? 

(G) What objections are there to the use of the exclama- 
tion point ? 

(7) Write {a) an exclamatory-declarative sentence; {b) an 
exclamatory-interrogative sentence; (r) an exclamatory- 
imperative sentence. 

(8) Explain the meaning of syntax. 

(9) What is meant by the statement that tJic sentence is 
the unit of thought ? 

(10) On the left of a vertical line write five modified 
subjects, and on the right five suitable modified predicates. 

(11) Explain in what way you would teach pupils to dis- 
tinguish subjects from predicates. 

(12) Give a rule for the choice of words in expressing 

your thought. 

§3 



3 PEDAGOGICS OF GRAMMAR. § 3 

(13) Explain exactly what is meant by the word modifi- 
cation as it is used in grammar. 

(14) Distinguish between qualify and liuiit. 

(15) Analyze by mapping and by diagram : 

" Maud Muller on a summer's day 
Raked the meadow sweet with hay." 

" The evil that men do lives after them; 
The good is oft interred with their bones." 

(IG) Explain what is meant by general modification as 
applied to words in a sentence. In what respect does it 
differ from grammatical jnodificatioii / Illustrate. 

(17) Classify sentences with respect to form, and with 
respect to use. Give illustrations. 

(18) Tell, in your own language, what is meant by the 
extension and the comprehension of common terms. 

(l!)) Analyze by diagram, but do not dismember, the 
following sentence : 

" He was like some one lying in twilighted, formless pre- 
existence, andstretching out his hands lovingly towards many- 
colored, many-sounding life. " 

(20) Contract the following into simple sentences: 
"He had a very noble old age, and grew daily better 

known to people that lived in the cities of the plain." 

"A time comes for all men when the helm is taken out of 

their hands." 

' ' The children were playing in the churchyard where the 

grass was green. " 

(21) Rewrite the following so that it shall contain no 
independent elements: 

"Self-reverence, self-knowledge, self-control, 
These three alone lead life to sovereign power. " 

(22) Explain in what respect the study of grammar has 
practical value. 



§ 3 PEDAGOGICS OF GRAMMAR. 3 

(23) What subdivision of grammar is it that treats spe- 
cially of sentences combined in paragraphs and other con- 
nected composition ? 

(24) What are restrictive clauses, and what are coordinate 
clauses ? Illustrate each. 

(25) By means of diagrams show the difference in respect 
to form of the following sentences : 

"The house, which my father owned, was burned yester- 
day." 

"The dog that bit the boy was killed by a policeman." 

(26) Explain imder what circumstances ambiguity is 
likely to result from the use of pronouns. Illustrate. 

(27) Prepare a scheme to be put upon a blackboard for a 
lesson in the synthesis of sentential elements. Explain how 
it should be used. 

(28) Explain the difficulty in defining subject and predicate. 

(29) What is meant by pleonasm ? Give two oi'iginal 
examples, and two that are quoted. 

(30). Write five complex sentences, using in each a dif- 
ferent connective. 

(31) Explain what is meant hy false syntax. Give five 
examples. 

(32) State the exact difference between a simple sentence 
and a compound sentence. Illustrate each. 

(33) Write {a) a compound declarative sentence; {b) r 
compound interrogative sentence ; (r) a compound imperative 
sentence. 

(34) Write a simple sentence having subject, predicate 
verb, and object, compound. 

(35) Give, in your own words, the substance of the para- 
graph on the "Order of Sentential Elements." 

(30) Supply connectives, if necessary, and arrange the 
following elements with a view to the best effect. Give 
reasons for your arrangement. 



4 PEDAGOGICS OF GRAMMAR. § 3 

Her sails rent by storms 
A ship entered Chesapeake Bay- 
Once upon a time 
IVIore than 250 years ago 
With a cargo of slaves 
On a beautiful June morning. 

(37) Distinguish clearly between syntax and etymology. 

(38) What disadvantage arises from treating etymology 
and syntax separately ? 

(39) State some objections to etymological parsing. 

(40) Explain fully the distinction between sex and gender, 
and illustrate by sentences in which both words are correctly 
used. 

(41) Criticize the following definition: "A noun is the 
name of any person, place, or thing that can be known or 
mentioned, or that can be conceived by the mind." Write 
such a definition as you would approve. 

(42) Explain two of the devices used in what is called 
"sentence building," and tell how you would employ. them 
in teaching grammar. 

(43) Explain a good working method of systematically 
enlarging a pupil's vocabulary. 

(44) If a child uses for the first time an objectionable 
word, should he be warned to avoid the word, or would it be 
better to ignore the matter ? Why ? 

(45) Should or should not young pupils learn grammat- 
ical definitions ? Why ? 

(4G) What important objection can be urged against 
most systems of grainmatical diagrams ? 

(47) Find ten substitutes for nice as commonly used, and 
write expressions in which each appears as a modifier. 

(48) Describe an exercise intended to enlarge the pupil's 
vocabulary. 



PEDAGOGICS OF GRAMMAR. 



(PART 2.) 



(1) Explain and illustrate what is meant by relation in 
grammar. 

(2) Define the pronoun, mention the principal classes, and 
give examples of each class. 

(3) In how many senses may the following sentence be 
understood ? 

" Mr. A told Mr. B that he ought to engage a man to take 
care of his horses." 

Write them all so that they cannot be misunderstood. 

Rewrite the sentence in the best manner, so that it shall 
mean that the horses belong to Mr. A and that Mr. B is to 
engage the hostler. 

(4) Explain the meaning of 



A 
The 

A 
The 



son of 



a 
the 
the 

a 



- poor widow. 



(5) What is meant when we say that an adjective viodifies 
the i/ieaning of a noun, as in the expression small hoy ? 

(0) Without using prefixes, write ten pairs of adjective 
antonyms. 

(7) Prepare a suitable blackboard drill, in some such form 
as is shown in Art. 43, to teach the difference between don't 
and doesn't, and in the drill use all the suitable pronouns. 

§4 



2 PEDAGOGICS OF GRAMMAR. § 4 

(8) Find five adjectives, each of which shall be a mean 
between extremes, and give the extremes. 

(9) Prepare a blackboard drill the object of which is to 
teach pupils to use the irregular verb lie (to recline) correctly. 

(10) Write five sentences in which verbs usually active 
are employed as neuter verbs. 

(11) Write five sentences in which the verb is used both 
as active and as neuter, indicating each use by modifiers. 

(12) Explain the term active as used with reference to 
verbs, and illustrate. 

(13) Write the inflection of the first personal pronoun. 

(14) Distinguish between the comparative and the super- 
lative degree. 

(15) What must a declarative sentence contain in order 
that the verb shall be regarded as transitive ? an imperative 
sentence ? Illustrate. 

(16) Explain why it is impossible fully to define the verb. 

(17) Write the principal parts of see, drink, ring, come, 
eat, be, run, sing, zvrite, find. 

(18) Give ten of the adverbs most frequently used with 
adjectives to indicate degrees of comparison other than those 
called regular. 

(19) What are the principal means of adding new words 
to our language ? 

(20) Why are the irregular verbs more forcible than the 
regular verbs ? 

(21) By means of a diagram analyze the following 
sentence : 

"Yet I doubt not through the ages one increasing purpose 
runs, 
And the thoughts of men are widened by the process of 
the suns." 

(22) Show a tabular classification of the pronoun. 



§ 4 PEDAGOGICS OF GRAMMAR. 3 

(23) By means of prefixes write five pairs of antonyms. 

(24:) Explain what is meant by approximation and liiini- 
nation in arriving at tlie exact meaning of words. Illustrate. 

(25) Beginning with the weakest, prefix the following 
words to the adjective sick^ in the order of their degree 
of meaning: very, quite, exceedingly, positively, uiiiisually, 
extremely^ extraordinarily, deeidedly. 

(2G) Explain and illustrate what is meant by asserted and 
I5y assui/ied predication. Mention the forms of the verb in 
which the predication is of the latter kind. 

(27) State the idea most conspicuously expressed by each 
of the several modes. Illustrate. 

(28) Write five sentences, each containing a verb that is 
really in the subjunctive mode. 

(20) " Would, indeed, we had been. 

In lieu of many mortal flies, a race 
Of giants, living each a thousand years. 
That we might see our own work out, and watch 
The sandy footprint harden into stone." 

[a) Tell the mode and the tense of each verb in the fore- 
going. 

{b) Give the syntax — that is, explain the function— of 
race; oi years ; oi out ; oi indeed. 

(c) Classify the sentence with respect to form; with 
respect to 2ise. 

(d) What is the subject of ivonld ? of harden ? 

(30) In what way may a modal adverb be distinguished 
from an ordinary adverb .? Write five sentences, each con- 
taining a modal adverb. 

(31) Write a synopsis of the verb come in the indicative 
mode, first person, singiilar. 

(;)2) Give two rules for the use of sJiall and will, and 
write illustrative sentences. 



4 PEDAGOGICS OF GRAMMAR. § 4 

(33) In what sense were shall and xvill originally nsed, 
and what changes have they undergone ? 

(34) Write five sentences, using in each both should and 
ZOOllld. 

(35) Explain the meaning of each of the following: 
{a) " If you should come, I would return with you." 
(/;) " If you would come, I should return with you." 
{c) "I will go, and nobody shall prevent me." 

{d) " I shall go, and nobody will prevent me." 

(3G) Which of the following is correct ? Give reasons 
for your answer. 

" If the time should ever come, etc." 
" If the time would ever come, etc." 

(37) Write sentences, using the following, first as adverbs 
and then as prepositions: off, by, near, above, over. 

(38) Write two sentences containing verbs in the infini- 
tive, the infinitive having a subject and an object. 

(39) Correct the following sentences, and give the 
reasons for your corrections: 

{a) " We certainly expected to have called." 

{b) "I would be very glad to have seen him." 

(<f) " There is no doubt but that the enterprise will be 

successful. " 

{d) " If it will come to pass that he shall consent, I will 

be much gratified." 

(40) What time of action or state is denoted by the verbs 
in the following sentences ? 

[a) " If he were here, it would be well." 

{b) " Should he arrive on time, we may depart at once." 

{c) "Were he a giant, I should withstand him." 

{d) " ' To be or not to be' ought not to have worried 

Hamlet." 

(r) " He may have erred, but it might have been through 

ignorance. " 



§ 4 PEDAGOGICvS OF GRAMMAR. 5 

(41) Classify the participles, and write five sentences, each 
of which contains one or more participles. 

(42) Write a list of ten interjections in which the sense is 
echoed by the sound. 

(43) Write five compound sentences, using five different 
coordinating conjunctions. 

(44) Use in sentences the following, first as adverbs, and 
tten as conjunctions: ic/uii, initil, i^'Jicrc. 

(45) Write sentences containing the following words, 
accompanied by appropriate prepositions: suitable, repug- 
nant^ solieitous, respectful^ contented. 



PEDAGOGICS OF GEOGRAPHY. 



(1) Define value in general, and explain why it is extremely 
difficult to fix a standard of value in educational subjects. 

(2) Explain what is meant by the " New Education." 

(3) Explain fully what is contemplated in Commissioner 
Harris's " Classification of Studies." Give his classification. 

(4) To what circumstances is owing the present great 
value of a knowledge of geography, as compared with its 
value fifty years ago ? 

(5) What is the psychological value of geographical 
study ? 

(6) Mention the sciences that have in their names the 
Greek word yf/, gc, and briefly explain the scope of each of 
these sciences. 

(7) Explain and illustrate the meaning of spccializaticvi 
in education. 

(8) What studi-es besides geography are included in a 
complete study of inorganic nature .? 

(0) Explain why wc may expect geography to increase 
in educational value with the lapse of time. 

(10) Why cannot a course of study be established that 
shall be equally suited at every period for all students ? 

§5 



2 PEDAGOGICS OF (GEOGRAPHY. §5 

(11) In your own words, explain the criterion having the 
highest value in- estimating the educational worth of geo- 
graphical facts. 

(12) What are the two chief aspects in which the earth 
may be studied ? 

(lo) Distinguish fully between physiography and physical 
geography. 

(14) Write a fundamental outline of the subject of gen- 
eral geography. 

(15) Explain what is meant by the expression "The 
Correlation and the Conservation of Energy. " What is the 
primary physical source of all energy ? 

(IG) Tell why it is necessary for the teacher of geography 
to be fully acquainted with the physical sciences generally. 

(17) Explain the need for sense training, and illustrate 
by citing some remarkable examples of proficiency attained 
in this kind of culture. 

(18) Describe fully what is meant (^?) by sensation^ and 
{b) hy perception. 

(10) Give fully the threefold classification of sensations. 

(20) Give in your own words an outline of the paragraph 
on " The Importance of Attention in Observing." 

(21) Describe the Greek pedagogue and his work. 

(22) What are the duties' of the parent towards the child 
while it is getting its first notions of the things around it .-' 

(23) What is the educational value to the child of outdoor 
life ? Mention some of the diflficulties in the way. 

(24) Explain how pictures may be prepared, and the man- 
ner in which they should be used in teaching geography. 

(25) In preparing for the study of geography proper, 
what kind of use shoiild be made of the natural sciences ? 



§ 5 PEDAGOGICS OF GEOGRAPHY 3 

(20) Describe the kind of help in his work that a teacher 
of geography may obtain from the government of the United 
States. 

(27) Describe some iisefvU series of specimens that would 
be helpful in teaching geography. 

(28) Give the substance of Sir Archibald Geikie's remarks 
oil the kind of preparation that a teacher of geography should 
have. 

(29) As a preparation for the study of geography, what 
training should children have in the imits of measure ? 

(30) How would you lead your pupils to an adequate con- 
ception of a square mile ? What surface of greater extent 
could be used as a imit of measure in comparing the areas 
of countries ? 

(31) Of what use in the study of geography is the knowl- 
edge of angular measurement ? 

(32) Make of good paper a protractor, and with it con- 
struct a triangle having angles equal to 75°, 45°, and 00°. 
Afterwards, paste your protractor to your examination paper 
near the triangle. 

(33) Construct a circle, and then draw and mark radii to 
represent sixteen of the most important points of the mar- 
iner's compass. Do the work as neatly as you can. 

(34) Explain wdiat is meant by " Mercator's projection," 
and tell what are the objections to its use in teaching- 
geography. 

(35) Tell in what way the bicycle can be made use of in 
teaching local geograph}'. 

(36) Give the substance of Rousseau's remarks on the 
importance of teaching not words but things. 

(37) Describe some simple and easy observations on the 
apparent motion of the sun, and tell what may be taught 
from them. 



4 PEDAGOGICvS OF GEOGRAPHY. § 5 

(38) What degree of finish and accuracy should be 
required of pupils in the maps they draw in their course in 
geography ? 

(39) Give the substance of the resolutions on the subject 
of map-drawing, adopted by a certain German Geographical 
Congress. 

(40) Make a series of squares to show the comparative 
areas of the New England and Middle Atlantic states. 

(41) What is meant by the expression "Sailor Geog- 
raphy " ? 

(42) Write five questions in geography that you regard 
as illustrative of important geographical facts, and five that 
you deem trivial and unimportant. 

(43) Indicate clearly what you regard as evidence of a 
good textbook in geography, telling what you would expect it 
to contain, and also some of the things that should be absent. 

(44) Give five important points to be observed in teach- 
ing geography. 

(45) Explain the importance of map reading, and tell 
what a map should finally represent to the pupil. 

(46) What should be some of the conspicuous character- 
istics of a good map for classroom use ? 

(47) What important points in the teaching art can be 
gathered from the model lesson given in Art. 9G V* 

(48) Prepare an outline of a lesson to be given on the 
map of Pennsylvania, and state in order the points that you 
would develop. In doing this, assume that your pupils are 
familiar with the general geography of the United States, 
and have now begun a study of the states in detail. 

(49) Illustrate what is meant by cause and effect in 
geography. 

(50) State the importance to the teacher of skill in the 
art of questioning, and describe the classes of questions that 
are employed in teaching. 



PEDAGOGICS OF HISTORY. 



(1) Define the four principal forms of composition. 

(2) Which of these forms should be found in historical 
writing- ? 

(3) What is meant by iini/iiual composition ? Mention a 
famihar unilineal poem. 

(4) Is Whittier's "Maud Mullcr" unilineal, bi/inral, or 
inultili>ical f 

(5) In history, what is meant by chronological sequence ? 
Write about 100 words describing- a fishing- trip, and observe 
chronological sequence in your description. 

((») What is meant by the order of cause and effect ? Out- 
line a supposed case in which this order is observed. 

(7) Explain briefly why it is so difficult to write an inter- 
esting and intellig-ible historical textbook. 

(8) State why some school studies are liked by children 
and some are not. 

(9) Explain why it is easier to teach arithmetic success- 
fully than it is history. 

(10) What are the principal advantages to be derived 
from a thorough knowledge of the history of one's own 
country ? 



2 PEDAGOGICS OF HISTORY. § 6 

(11) In what respects is a student more benefited by a 
familiarity with general history than he is by knowing the 
history of his own country ? 

(12) vState, briefly, the qualifications necessary in a teacher 
of history. 

(lo) Explain what effect the perfecting of submarine 
navigation would be likely to have upon naval warfare in 
the future. 

(14) Mention five works, not school textbooks, that you 
would advise a teacher of history to read, and state what 
benefit would be derived from each. 

(15) Give the titles of five familiar poems, not mentioned 
in the Instruction Paper, that a teacher of history could 
advantageously use with his class. 

(IG) Explain the advantages derivable by students of his- 
tory from reading historical novels. 

(17) Mention the titles of five valuable historical novels. 

(18) What is meant by the " Story of Scheherezade " ? 

(10) Explain what is meant by the "historic sense." 
Mention three of its principal phases. 

(20) What advantage may be derived from the use of 
myths in teaching history ? At about what age of the pupil 
are myths and fairy tales valuable ? 

(21) How is biography used in teaching history in Ger- 
many ? 

(22) State the usual objections against memorizing- a his- 
tory lesson in the exact words of the author. 

(23) Prepare a list of ten questions suitable for use as 
"historical recreations" in United States history. 

(24) Describe, in outline, the Biographical method as it 
is employed in Germany. 



§ (5 PEDAGOGICS OF HISTORY. 3 

(^5) Under what circumstances is the Catechetical method 
to be condemned ? 

(26) Describe in your own language the Laboratory 
method. 

(37) Give an outline of the entire German course in 
history. 

(28) What are the chief obstacles to be overcome in using 
the Lecture method, and how may they be overcome ? 

(20) What do you inidcrstand by the "ethical sense" in 
history ? Illustrate. 

(30) How would you proceed to awaken and develop the 
ct Ideal sense ? 

(31) State two psychological facts that necessitate fre- 
quent reviews. 

(32) Cite two historical illustrations of the principle that 
luijust treatment of the weak and defenseless results, sooner 
or later, in the discomfiture of the stronger. 

(33) vState the underlying principles that should control 
the method of a teacher in conducting a history lesson with 
a class of young pupils. 

(34) Referring to (33), what are the methods of securing 
the ends desired ? 

(35) Give, in your own language, the reasons for begin- 
ning with the Biographical method earlier than is done in 
Germany. 

(36) Describe in outline the Comparative method. 

(37) Of the various methods described in the Instruction 
Paper, which, in your judgment, is the best ? Give your 
reasons. 

(38) Explain and illustrate the application of the division 
of labor in teaching. 

(30) What are some of the objections urged against the 
division of labor in teachino: ? 



4 PEDAGOGICS OF HISTORY. § 6 

(40) What is meant by the term correlation when applied 
to branches studied in schools ? 

(41) Explain, briefly, the correlation of history with phys- 
ical geography. 

(42) What subjects, besides those mentioned in the 
Instruction Paper, are correlated with history ? State in 
what respect. 

(43) Why may not all the subjects in a curriculum be so 
correlated as to be taught at the same time ? 

(44) What objections are there against using the story of 
" Robinson Crusoe " as a correlation center ? 

(45) Explain in what respects the subjects of sociology, 
civics, and ethics may be correlated with history. Which is 
the most important correlation ? 



PEDAGOGICS OF ORTHOGRAPHY. 



(1) How is orthography related in classifieation to 
grammar ? 

(2) State in detail what subjects are included under 
orthography. 

(3) Explain what is meant by "a perfect alphabet." 

(4) How is a nation's progress in civilization affected by 
the character of lang'uage ? Illustrate. 

(5) Write the approved singular and plural forms of the 
names of the vowels. 

(6) Give the plural of the following: A, &, q, [], X. 
Express in words the meaning of the plurals you have 
written. 

(7) Write ten words, of which five illustrate an easy, and 
five a difficult, coalescence of sounds. 

(8) What are the chief advantages to be derived from a 
knowledge of correct syllabication ? 

(9) Prepare a list consisting of twenty words of difficult 
syllabication, and, by hyphens, divide them properly. 

(10) Write directions such as a young teacher should need 
in conducting an oral spelling lesson. Let these include 
{a) the teacher's directions to the pupils, and (b) the rules 
of procedure that he himself should observe. 

(11) Prepare a list of {a) ten solid compound words; 
{b) ten approved hyphenated compounds. 

§ 7 



% PEDAGOGICS OF ORTHOGRAPHY. § 7 

(13) Through what three stages of union do two words 
pass in forming finally a solid compound ? Hlustrate. 

(13) What change of accent is usually made during the 
transition of two separate words to the form of a solid com- 
pound ? Give two illustrations. 

(14) Each of the following is ambiguous: ^^ black horse 
ti'oops," "■wild ivestern melodies,'' "• Poems Here at Home,'" 
"■ Freneh and English dictionaries.'" Write them so as to 
show with precision their various possible meanings. 

(15) Write five practical suggestions relating to com- 
poimd words. 

(16) Explain and illustrate the meaning of syndud, abbre- 
viation, and contraction. 

(17) Explain briefly the tw^o different impressions that 
may be made upon the mind by a word. Illustrate by ineans 
of a landscape. 

(18) Mention two distinct objects that should influence a 
teacher in selecting lists of words for work in orthography. 

(19) Under what conditions is it better for the teacher 
himself to prepare lists of words for the orthographical work 
of his own pupils ? 

(20) Designate the three principal uses that words serve. 
Which is the easiest to master and which the most difficult ? 
Give reasons for your answers. 

(21) Give and illustrate three of the most useful rules for 
spelling. 

(22) Indicate by diacritical marks the sounds of the 
vowels, and illustrate each soimd by a word that contains it. 

(23) Give in outline a plan of proceeding in an ordinary 
spelling lesson. 

(24) Indicate what should be required of a pupil in spell- 
ing orally the word refractory. 



§ 7 PEDAGOGICvS OF ORTHOGRAPHY. 3 

(25) Explain why pupils should not be required to write 
the same words many times for punishment or for other 
purposes. 

(20) What is the "Flash method" in teaching- spelling? 
Mention one objection against this method with one reason 
for the objection. 

(27) Mention the four principal methods of making chil- 
dren acquainted with the meaning of words. 

(28) Construct sentences that will show by the method 
of particular instance — by context — the most usual meanings 
of the following words: division^ mutual^ deception^ rapidly^ 
honesty. 

(20) Explain how English spelling is correlated with 
every other subject that is taught in our language. 

(30) Explain and illustrate the formation and meaning of 
English diminutives. 

(31) By means of diacritical marks indicate the pronunci- 
ation and syllabication of the following words: Aristidcs, 
obligatory, pharyngeal, maniacal, financial. 

(32) Use the following words with suitable prepositional 
phrase modifiers, denoting that to which each term is 
usually applied : band, horde, eonneil, congress, troop, squad, 
detail, brace, gang, cloud. 

(33) Find the nearest opposites, without prefixes, of the 
following woids: indolent, agile, courteous, publicity, liberal, 
candid, dormant, truthful, stupid, humility. 

(34) Give the names, difficult to spell, {a) of ten animals; 
{b) of ten plants; {c) of ten minerals. 

(35) Give words descriptive of the qualities of an apple, 
as follows: qualities perceived {a) by the sense of sight; 
{b) hy the sense of taste; {c) by the sense oi feeling. 

(30) Of words suitable for a spelling exercise, write 
{a) ten denoting animal products; (/;) ten denoting vege- 
table products. 



4 PEDAGOGICS OF ORTHOGRAPHY. § 7 

(37) Write the abstract nouns that contain the same root 
elements as the following: sphere, Jinaniinoiis, timorous, 
loquacious, porous, fierce, heroic, cowardly, perverse, opaque. 

(38) Prepare a list of the verbs that would likely be 
required in describing {a) a picnic; {b) a day at school. If 
any are transitive, write the probable object of each. 

(39) Describe an important use of pictures in language 
teaching. 

(40) Annex to each of the following adjectives a phrase 
modifier, beginning each with a suitable preposition: redo- 
lent, delighted, ■ friendly, neigliborly, fastidious, capricious, 
renoivned, actuated, suitable, uncertain. 

(41) Explain tipon what three circumstances depends the 
question as to what preposition shall be used with particular 
words. Illustrate. 

(42) Find adjectives or verbs after w^hich each of the fol- 
lowing prepositions may be used: concerning, betivcen, among, 
after, against, toivard, in, into, respecting, regarding. 

(43) Write the names of ten American authors with whose 
-v^ritings a cultivated citizen should be familiar, 

(44) Write correctly twenty geographical names whose 
spelling you regard as difficult and important. 

(45) Prepare a list of fifty words commonly mispro- 
nounced, but not found in the Instruction Paper. 



INDEX. 



Note.— All items in this index refer first to the section (see Preface) and then to the 
page of the section. Thus, "Prosody 3 13" means that prosody will be found on page 13 
of section 3. 



A. 

A reminiscence 

A year's work 

Abbreviated division, General 

method of 

Abbreviations, Abuse and use of 
" and contractions 

" in denominate 

numbers 

" in metric system 

" Lessons in 

" Mixed 

" Pluralizing 

" The meaning of.. 

" The period with 

" used in science . . 

Abode of life. The earth as the.. 

Absolute possessive pronouns.. . 

Abstract nouns 

Abuse of the idea of place 

" " utilitarianism 

Accents, Primary and secondary 

Acquiring a vocabulary 

Action and state 

" Cause and consequence 

of historic 

" Predicated or assumed . . 
Active and neuter. Verbs that 

are both 

" intransitive verbs 

" transitive verbs 

Adding and subtracting frac- 
tions by inspection . . . 

" by groups 

" horizontally 

" two or more columns 

at once 

Addition and subtraction in one 
operation 



St-c. 


Pa.irt' 


5 


12G 


1 


09 


2 


23 


r 


33 


7 


31 


2 


69 


2 


70 


7 


83 


7 


34 


7 


3G 


7 


33 


7 


35 


7 


3(3 


5 


3.5 


■4 


(i 


3 


7() 


5 


29 


7 


41 


7 


28 


3 


63 


4 


38 


6 


42 


4 


43 


4 


7.5 


4 


3.5 


4 


35 


o 


45 


2 


5 


o 


5 


o 


6 


o 


3 



Addition, Drill work for 

" of denominative num- 
bers , 

" of long columns 

" Proofs of 

Adjective, Derivation and office 

of the 

" Inflection of the 

" pronouns 

" " Demonstra- 
tive 

" " Distributive 
" " Interroga- 
tive 

" " Possessive.. 

Table of the 

Adjectives and adverbs as re- 
lated to verbs 

" Brown's classifica- 
tion of 

Cardinal 

Classification of 

Common 

Comparison of 

Compound 

Criticism of Brown's 

classes of 

Meiklejohn's classi- 
fication of 

Numeral 

Ordinal 

Participial 

Pronominal 

Proper 

Qiialitative 

Quantitative 

Remarks on table of 
Serial 



Sec. 
1 



28 

64 

1 

2(J 

10 

17 
6 

15 
15 

15 
15 
16 





14 




14 




15 




14 




13 




13 




14 




14 




17 




24 



INDEX. 



Src. Pjire. 

Advanced work, Methods in ~ 1 

" '■ with formulas.. 1 ~G 
Advantages with duodecimal 

scale 1 45 

Adverb, Conjunctive 4 It 

" Interrogative 4 70 

Modal 1 r; 

" Position of the 4 7'8 

" Simple 4 T6 

Table of the 4 79 

The 4 73 

Adverbial elements in conjunc- 
tions 4 sr 

" objectives 4 78 

Adverbially, Prepositions used.. 4 81 
Adverbs classified with respect 

to meaning 4 78 

" classified with respect 

to u.se 4 70 

Adversative conjunctions 4 80 

Aliquot parts, Division by 2 15 

" " Extension by 2 14 

" " Method of, in in- 
terest 3 82 

" " Multiplication by 2 13 

Alphabet, A perfect 7' 

Alphabetical arrangement of 

suffixes 7 87 

Alphabets 7 2 

Alternative conjunctions 4 80 

Ambiguity 3 41 

" from vise of pronouns 4 7 
" Use hyphen to avoid 7 30 
American Philological Associa- 
tion 7 10 

Amount of work less important 

than method 1 70 

An early requirement in geog- 
raphy 5 08 

Analysis by diagrams 3 28 

" Models of 3 29 

" of sentences 3 27 

" Remarks on method 

of 3 35 

" Review of details in . . . 3 32 

"And," Use of, in numeration. . . 1 44 

Anecdote of Hogarth 1 5 

Angles, Measuring and con- 
structing 5 75 

Anglo-Saxon prefixes ■... 4 25 

Angular measurement 5 73 

Annual interest 2 87 

Antonyms 4 23 

" by prefixes 4 20 

Apparatus, Legitimate use of, 

for illustration 1 15 

Apparent motion of svin 5 93 

Appliances, Concrete . , 1 11 



Sec. Page. 
Application of abbreviated divi- 
sion to G. CD. 2 41 
" " drills to practical 

work 1 30 

Applications of percentage 2 77 

Applied number. The 1 73 

Approximation 2 30 

Arabic notation 1 38 

Argument 3 

Arithmetic, Advanced 1 4 

" Elementary- 1 4 

" Intermediate 1 4 

" Pedagogics of 1 2 

" Primary 1 3 

" Schemes for earliest 

work in 1 5 

Arithmetical language, (Gram- 
mar of 1 17 

" progression 2 115 

" stories 1 22 

" 1 53 

study, Divisionsof 1 3 
Art and .science, Distinction be- 
tween 1 3 

" of questioning. The 5 123 

Article in " Forum" on spelling 7 51 
" " "Forum " on spelling. 

Criticism of 7 54 

" " "Forum " on spelling. 

Remarks on 7 53 

Articles 4 15 

Assistance, Illicit, by the teacher IS 

Assumed action 4 43 

Attention, Importance of 5 47 

" Voluntary 1 4 

Authority of dictionaries. 7 31 

Auxiliary verbs 4 66 

Average requirements in educa- 
tion, Approximation of 5 18 

B. Sec. Page. 

Bank discount 2 93 

Barbauld, Mrs 5 41 

Bases of notation 1 44 

Basis of science. Ultimate 5 36 

Beethoven 5 41 

Bicycle notes 5 85 

" Surveying with 5 83 

" The, in geography 5 81 

trip. Map of 5 88 

Bilineal writing 6 4 

Biographical method 41 

" " a s a d V o- 

cated by 

Herbart 50 

" reading 5 14 

Blackboard, Drill schemes for. . . 1 28 

" in teaching 1 10 



INDEX. 



XI 



Sec. Page. 

Books of reference 5 i;W 

" " '■ in country 
districts. . . . ]() 
" " travel and adventure . . 5 133 
" '' " geography.. 5 134 

Botanical help.s -5 63 

"Bread-and-Butter " Sciences, 

The 5 15 

Brevity, T'orce gained by 3 55 

Brooks', Dr., method of cube 

root 2 108 

Brown, Dr. Goold 4 15 

Building, Sentence 3 48 

Business multiplication 2 10 

C. Sec. Page. 

Camera in geography. The 5 56 

Canada, Interest laws of 2 94 

Canceling in fractional work 2 51 

" simplified 2 52 

Capital-and-boundary in geog- 
raphy 5 110 

Capitals and punctuation 3 14 

Cardinal numerals 4 15 

Care in use of relatives 3 44 

Carrying 1 30 

Case, Definition of 3 81 

Cases 3 81 

" Ntimber of 4 2 

Catechetical method 6 2" 

Cause and consequence 6 42 

" effect 2 97 

" " " in teaching ge- 
ography 5 122 

Causes on which the value of 

geography depends 5 20 

Certain prepositions, Misiise of. . 4 84 
" words, Use of preposi- 
tions with 4 8:3 

Changmg rates of interest 2 85 

Children, Distaste for history in 6 

Chinese language. The 7 3 

Circle 2 110 

" Use of, in drills 1 29 

Classes of interjections 4 89 

" nouns 3 74 

" " pronouns 4 5 

Classification of adjectives, A 

new 4 10 

" " adjectives. 

Brown's 4 13 

" " adjectives, 

]\Ieiklejohn's 4 11 
." " adverbs with 
respect to 

use 4 76 

" " orthographical 

work 7 82 



Sec. Page. 

Classification of participles 4 .56 

" ■' processes iti 

d e nominate 

numbers .... 2 60 

" " questions 5 124 

" " questions. Re- 
marks on 5 125 

" " sensations 5 43 

" " sentences, 

Connectives 

in 3 57 

" " sentences. 

Summary of 3 56 
" " sentences with 
respect to 

form 3 20 

" " sentences with 

respect to 

use 3 18 

" " studies. Com- 
pleteness of. . 5 12 
" " studies. Gen- 
eral '5 10 

" " verbs 4 32 

" " " Remarks 

on 4 40 

Classroom drawn to scale 5 79 

Clay modeling 5 100 

Clubs, Historical 6 35 

Coalescence of sounds 7 8 

Cobbett's grammar quoted 4 31 

Collecting devices for teaching 

orthography 7 .53 

Collection of examples with 

"Shall "and "Will" 4 72 

Collections in natural science ... 5 60 

" Miscellaneous 5 05 

" of false syntax 3 62 

" Words denoting 7 93 

Collective nouns 3 76 

Column spelling 7 46 

Columns, Addition of 1 29 

Comenius, A maxim of 7 40 

" Maxim of 5 41 

" Committee of Fifteen " 5 24 

05 

"Committee of Fifteen," Re- 
marks on report of 6 67 

Common adjectives 4 13 

" tisage 3 52 

" use, Words in 7 58 

Comparative and superlative. 

Forms of the 4 28 

" degrees of adjec- 
tives ; 4 21 

" importance of sen- 
tential elements 3 69 
" method, The 6 52 



Xll 



INDEX. 



Comparative methods, Remarks 

on 

Comparison of adjectives 

" " rules for partial 

payments 

" Other expressions 

of 

Comparisons, Pictured 

Compass, The mariner's 

Complement, Predicate 

Complete living 

Complex sentence 

" sentences. Synthesis of 
Composite numbers, Study of... 
Composition, Historical, consists 

of 

" S en t e n ce s com- 
bined in 

Compound adjectives 

" interest 

" predicate 

" pronouns 

" sentence 

sentences,Mapping of 

" subject 

" " in predicate.. 

" words,Evolution of... 

" " Exercises with 

" " Inconsistent 

forms of 

" " Remarks on... 

CompoundinK' of words 

" " " Perplex- 

ing na- 
ture of 
" words, Rules for 

Compounds, Creek and Latin... 

" Hyphened 

Solid 

Comprehension 

Concepts from pictures 

" in elementary science. 

Conclusion 

Concrete appliances 

Conditions affect e d u c ational 

values 

" expressed by sym- 
bols 

" of success in history, 

The 

" " success in teach- 
ing fractions 

Congress, Geographical 

Conjunction, The 

Conjunctions, Ad V e rbi al ele- 
ments in.- 

" Adversative 

" Alternative 



Sec, Page. 



4 


22 


5 


102 


5 


75 


3 


33 


.5 


16 


3 


24 


3 


54 


1 


8.5 



3 


12 


4 


14 


2 


88 


3 


23 


4 


7 


3 


23 


3 


ai 


3 


22 


3 


2;i 


7 


27 


7 


90 


7 


27 


7 


30 


' 


20 


r. 


20 


7 


22 


7 


31 


7 


20 


7 


20 


4 


10 


5 


57 


5 


40 


6 


72 


1 


11 



1 


21 


G 


58 


1 


49 


5 


90 


4 


85 


4 


87 


4 


80 


4 


86 



Sec. Page. 

Conjunctions, Copulative 4 80 

" Correlative 4 87 

•' Corresponsive 4 87 

Illative 4 87 

" Subordinating 4 87 

Table of 4 88 

The coordina- 
ting 4 86 

Conjunctive adverbs 4 77 

Connections 4 85 

Connective elements 3 33 

Consideration of spelling. Gen- 
eral 7 37 

Constructions, Special 3 .58 

Contractions 7 35 

" and abbrevia- 

tions 7 31 

Cooperative method, The 6 .55 

Coordinate clauses, Ambiguity 

from 3 41 

Correlation, M ean i n g of the 

term 6 65 

" of h i s t o r y w i t h 

ethics 6 71 

" "history with 

geography 6 09 

" "history with 

political science 6 70 
" " history with soci- 
ology 6 70 

" " s p el 11 ng w i t h 
general in for- 
mation 7 lot) 

Correlations of history 6 04 

" " spelling 7 80 

Correlative conjunctions 4 87 

" work, Objections 

to 7 99 

" " Remarks o n 

objections to 7 99 

Corresponsive conjunctions 4 87 

Cotton 5 64 

Country districts. Hooks of refer- 
ence in 6 16 

Critical stage, A 5 51 

Criticism, Ethical 6 43 

" of Brown's classes of 

adjectives 4 14 

" " definition of adjec- 
tives 4 20 

" " historical action. . . 6 43 

Crusoe, Robinson 7 80 

Cube root 2 100 

" " Dr. Brooks' method 

of 2 108 

Cyclometer 5 83 

" Surveying with bicy- 
cle and 5 83 



Xlll 



D. Sec. Page. 

Daily work, A 4 42 

Dates, Difference between 2 05 

IDecimal base of notation 1 44 

" " " Objections to... 1 45 

" method of percentage. . 2 72 

Decimals, Division of 2 25 

"Decimation" 1 29 

Declension 4 2 

Defecttve verbs 4 35 

Defining by opposites 7 74 

" " synonyms 7 74 

" words in connection 

with spelling 7 75 

Definition, Failure of 3 4 

" of case 3 81 

" " English grammar 3 3 

" "geography 5 27 

" "grammar 3 2 

" " language 3 1 

" "orthography 7 1 

" " subjunctive mode 4 47 

" " tense 4 58 

" " the adjective 4 11 

" " " preposition.... 4 79 

" " " pronoun 4 4 

" " verb 4 30 

Definitions of adjectives com- 
pared 4 20 

" " the noun 3 72 

Degree, Comparative 4 21 

Positive 4 19 

" Superlative 4 21 

Degrees of adjectives . 4 17 

" " predication by parti- 
ciples 4 57 

Demand for cause and conse- 
quence of action 42 
" " time of historic ac- 
tion G 42 

" " truth of narrative C 41 
Demrtistrative adjective pro- 
nouns 4 15 

Denominate numbers 2 .58 

" Abbrevia- 
tions of.. 2 1)9 
" " Addition 

of 2 04 

" " Classifica- 
tion of 
process- 
es in 2 00 

" " Division 

of 2 08 

" " Multipli- 
cation of 2 07 
" " Nature of 
factors 



Sec. Page. 
Denominate numbers, Order of 
subjects 

in 2 .59 

" " Subtrac- 
tion of.. 2 04 
Derivation and office of the ad- 
jective 4 10 

Description 1 

" of topographic sur- 
vey maps 5 107 

Detail in anal)-sis. Review of 3 32 

Determination, "Shall" and 

"Will " denoting 4 08 

Development of historic sense.. 45 

Devices and word lists 7 82 

" for teaching orthogra- 
phy. The collecting of 7 03 

Diacritical marks 7 .50 

Diagrams, Analysjs by 3 28 

" of multiplication 2 9 

Dialogue, Another specimen of 

Socratic 5 130 

Dickens, Charles ' 2 

Dictionaries, Authority of 7 31 

Dictionary, Standard 7 10 

Didactic questions 5 125 

Different aspects of same idea, 

Words denoting 7 94 

Difficult to teach history 8 

Difficulties 5 07 

Difficulty in syllabication 7 13 

Discipline and utility 7 01 

Discount, Bank 2 93 

" True 2 93 

Discounts, Serial 2 70 

Discrimination among facts, 

Necessary 5 111 

Discussion of rules 7 25 

Distaste for history by chil- 
dren 

Distinction between art and 

science 1 2 

" between mapping 

and analysis 3 27 

Distributive adjective pronouns 4 15 

Divisibility of numbers 2 33 

Division by aliquot parts 2 15 

drill. Development of. . 1 33 
" " General scheme 

of 1 35 

" " scheme in detail 1 35 

" French method of 2 4 

" 2 23 

" of interjections into 

classes 4 89 

" " labor in teaching ... C 02 

Proofs of 2 28 

" Short methods in 2 15 



See. 
Division slightly greater than 

10, 100, etc.. 3 
" " less than 10, 

100, etc 2 

" Special cases of 2 

Divisions of arithmetical studj-.. 1 

". "geography 5 

Divisor, Inverting the 2 

Drill and repetition. Necessity 

for 7 

" for addition 1 

" " division 1 

" " multiplication 1 

" " subtraction 1 

" " " General 

scheme of 1 

" with irregular verbs 4 

" without a purpose 1 

" work 1 

Drills applied to practical e.v- 

amples 1 

" Fundamental 1 

" in fractions. Useful 1 

" Purpose of 1 

Duodecimal base, Advantages of 1 

E. Sec: 

Earliest sensations, The 5 

" sense preceptions 5 

" work in arithmetic 1 

Early requirement. An 5 

Earth as a whole, The 5 

" " the abode of life 5 

Echo the sense, Interjections 4 

Eclectic method. The G 

Education, Specialization in 5 

" The new 5 

Educational fact modifies theorj^ 5 

" progress. Manner of 3 

" value of outdoor life 5 

" values 5 

Effect of writing the same word 

many times 7 

Element of place in geography.. 5 
" " success. Teacher's 

personality an 7 

Elementary arithmetic I 

Elements, Connective 3 

" Independent 3 

" Omitted 4 

" Order of sentential.. . 3 
" Synthesis of senten- 
tial 3 

Emerson, Ralph Waldo 

Ends of specimen lesson. Method 

of securing 6 

English grammar, Definition of 3 

" s}'nonj-ms, Works on. . . 7 



INDEX. 






Pii^e. 




Sec. 


Pajre 




Enlarging pupils' vocabularies. . 


3 


06 


19 


Environment of bicycle trip 

" Words belonging 


5 


89 


17 


to a given 


7 


95 


IS 


Equalization of factors 


2 
3 


106 


3 


Error as example 


60 


23 


Established usage 


7 


23 


54 


Estimate of place in geograph- 








ical value. Dr. Harris's 


5 


21 


65 


Ethical criticism 


6 


43 


28 


Etymological exercises involv- 




33 


ing spelling 


7 


95 


32 




3 


80 


30 




3 


67 




" and syntax. Com- 






31 


bined treatment of 


3 


69 


41 


" and synta.x, Treat- 






10 




3 

3 


68 


!) 


" Meaning of 


07 




Euclid's rule 


2 


114 


3G 


Every lesson a language lesson 


1 


71 


2S 


Evolution 


2 
9 


98 


05 


" by factoring 


102 


28 


" Equal factor method 






45 


of 

" Geometrical ilhistra- 


2 


103 


Pa.i,^^. 


tion of 


2 


102 


48 


" Methods of teaching. . 


2 


98 


40 


" of compound words .. 


7 


27 


5 


" " textbooks 


5 


112 


08 


Exact interest 


2 


86 


31 




5 


125 


35 


Examples, Collection of, with 




ss 


"Shall" and "Will" 


4 


72 


57 


" ■ of false syntax 


3 


61 


13 


" of subjunctive mood 


4 


49 


4 


" of subjunctivemood, 






10 


Remarks on 


4 


50 


G 


" Types of 


1 


)Si 


54 


l'3xclamatory sentences should 






1 




3 
3 


' 19 




Exercise in synthesis. Another.. 


49 


09 


" Synthetic, for increas- 






28 


ing vocabulary 

Exercises in fractions 


3 

1 


47 


.50 


" "syllabication 


7 


14 


4 


" with compound words 


7 


90 


33 


" " prepositions 


7 


97 


34 


" " rules of spelling. . 


7 


90 


30 




'' 


88 


51 


Existing conditions affect educa- 








5 
1 


8 


4G 


Experiment with objects 


14 


47 


Experimental questions 


5 


124 




Explanation of methods 


7 


74 


49 




f> 


2 


3 


Expression s of c o m p a r i s o n , 






75 


Other 


4 


22 



Sec. Page. 
Extension of meaning of "Top- 
ical" 6 32 

" " terms 4 10 

Extremes and means among 

words 4 23 

F. Sec. Page. 

Factoring 2 38 

Evolution by 2 102 

G. C. D. by 2 39 

Factors, divisors and multiples. . 2 38 

" Equalization of 2 100 

" Nature of, in denomi- 
nate numbers 2 70 

Facts of science should be dis- 
criminated 5 111 

False syntax, Collections of 3 62 

" " Examples of 3 01 

Fifteen, Committee of 5 24 

" 05 

First teacher, The child's 5 52 

Flash method in spelling 7 72 

Force gained by brevity 3 55 

Form and matter of letters 7 98 

" " punctuation of abbre- 
viations 7 31 

" Sentences classified with 

respect to 3 20 

Forms, Graphic geometrical 5 104 

" of comparative and su- 
perlative 4 28 

" " passive progressive. . 4 02 

" " pleonasm 3 59 

" " written thought 1 

" Other transitive 4 37 

Formulas, Advanced work with 1 20 

" in interest 2 78 

" " mensuration 2 110 

" percentage 2 75 

Type 1 25 

Formulated rules 7 25 

Formulating of operations 2 32 

"Forum," Article on spelling 

in 7 51 

" Criticism of article 

on spelhng in 7 .53 

Four, The number 1 77 

Fourth root 2 101 

Fraction method in percentage. . 2 75 

" work. Later 1 .53 

Fractional unit 1 8 

Fractions 2 45 

. " Addition and subtrac- 
tion of, by inspection 2 45 
" and integers taught 

to.gether 1 8 

" Caricelmg 2 51 

" Exercises in 1 7 



Sec. Page. 
Fractions, Greatest common di- 
visor of 2 55 

" Least common multi- 
ple of 2 57 

" Outline of plan of 1 50 

Roots of 2 101 

" Special cases in addi- 

tion and subtraction 

of 2 47 

" Teaching of 1 48 

" Written forms in 2 40 

French method of long division 2 4 

Fulton, Invention by 1 21 

Functions of the several modes. . 4 45 

Fundamental drills 1 28 

" meaningof "Shall" 

and "Will" 4 07 

" outline of geog- 

raphv 5 30 

Future participle, The 4- .58 

" tenses. The 4 01 

Futurity, "Shall" and "Will" 

denoting 4 70 

G. Sec. Page 

Geikie, Sir Archibald 5 07 

Gender of nouns 3 7'8 

" " sex 3 82 

(General considerations concern- 
ing spelling 7 37 

divisions of geography 5 33 

" information 5 48 

" " Correlation 
of spell- 
ing with 7 100 

" law of sequence 3 53 

" method of abbreviated 

division 2 22 

" modification 3 .39 

" principle in teaching, AG 7 
" scheme of subtraction 

drill 1 31 

" statement concerning 

abbreviations 7 31 

" treatment of lesson in 

orthography 7 07 

Geographical matter 5 20 

(ieography,"Capital-and- Bound- 
ary" 5 110 

" Correlation of his- 
tory with 09 

" Definition of 5 27 

" Fundamental out- 
line of 5 .30 

" Graphic 5 95 

" in pictures 5 50 

" Matter and method 



XVI 



INDEX. 



Sec. 
Geography, Physical science the 

essence of 5 37 

Pliny's 5 2G 

Sailor 5 109 

'• Some points in teach- 
ing 5 113 

The bicycle in 5 81 

" " term 5 26 

" " wheelman as a 

teacher of . . . . 5 82 

" without a textbook 5 08 

Geometrical forms, Graphic 5 104 

" illustration of evo- 
lution 2 102 

German geographical congress 5 90 
" school, A specimen les- 
son in a G 48 

Getting rid of objectionable 

words 3 65 

Gibbon, Edward 4 

Goethe 5 39 

Government by prepositions 4 81 

" surve}' maps 5 107 

Gradation in treating the 

noun , 3 70 

Cirammar, Brown's 4 31 

Cobbett's 4 31 

" Definition of 3 2 

" of arithmetic 1 17 

" Term "active" as 

used in 4 40 

" Terms used by wri- 
ters on 3 70 

Grammatical rules 7 23 

" study. Value of... 3 4 

Graphics of fractions 1 03 

Greatest common divisor by ab- 
breviated division 2 41 

Greatest common divisor by fac- 
toring 2 39 

Greatest common divisor of frac- 
tions 2 5.5 

Greek and Latin compounds. .. . 7 31 

'• pedagogue 1 1 

5 .51 

" prefixes 4 27 

Groups, Adding by 2 5 

Grube method 1 

H. Sec. Piiffe. 
Halves and thirds. First lesson 

in 1 51 

Harris, Dr. William T 5 10 

" " " " 5 17 

Harvard University 7 16 

Hearer, " Shall " and "Will " de 

noting will of 4 09 

" Heimatkunde " 5 91 



St'c. Page. 

Helps, Botanical 5 02 

Herbart, Biographical method as 

advocated by 6 .50 

Heredity in s^Delling 7 40 

Higher power, " Shall " and 

"Will " denoting will of 4 69 

Historic action, Cause and con- 
s e q u e n c e 

«f 6 42 

" " Criticism of.... U 43 

" " Time of 42 

Truth of 6 41 

" sense. Development 

of 6 45 

Historical and biographical 

reading 6 14 

" clubs 6 35 

" composition consists 

of... 3 

" recreations G 25 

" textbooks G 6 

" use of poems and bal- 
lads 6 23 

History, Children's dislike of.. . . G G 

" Correlations of G 64 

" Correlations of, with 

ethics 6 71 

" Correlations of, with 

geography G 69 

" Correlations of, with 

political science G 70 

" Correlations of, with 

sociology 70 

difficult to teach 6 S 

" Many methods in 6 27 

" Preparation for teach- 
ing 6 14 

" Purpose of studying. . . 9 
" Reasons for early be- 
ginning of G 51 

" Relation of, to other 

subjects 61 

" Time given to G 13 

" Vastness of 61 

Hogarth, Anecdote of 1 5 

Homer's "Catalogue of the 

Ships" 5 25 

" Hoosier .Schoolmaster," The. . . 7 38 

Horizontal addition 2 5 

How history is usually learned 17 

recited 6 18 
" teacher must regulate his 

reading 6 11 

Huber 5 41 

Human needs. Relation of science 

to 5 30 

Hyphen, to avoid ambiguitv. . . . 7 .30 

Use of 7 30 



INDEX. 



XVI 1 



I. Sn: Pas-,: 

Idea of place, Abuse of ."i 3 ) 

Illative conjunctions 4 hi" 

Illicit assistance by the teacher 7 18 
Illustrations of fractions, 

G raphic 1 63 

Illustrative lesson, Remarks on 6 49 

Imperative mode, The 4 64 

Impi)rtance of attention 5 47 

" " percentage 2 71 

" " sentential ele- 
ments. Com- 
parative 3 69 

Important and the trivial. The. . 5 108 

Improvement of method. The. . . 3 -.50 

Impulse to criticize 6 43 

Inconsistent forms of compound 

words 7 27 

Increasing vocabulary. Syn- 
thetic exercise for 3 47 

Indicative mode, The 4 44 

Inference from historic action.. . 6 43 

" Test of power of 6 44 

Inferiority of Roman notation.. . 1 47 
Infinitiveand participle. Similar- 
ity of 4 55 

" Complement of 4 55 

" mode. The 4 51 

" Sign of 4 53 

" " "to" as part of the 4 54 

" Subject of 4 51 

" Time denoted by 4 55 

Inflection of adjectives 4 17 

" " nouns 3 76 

Information, General 5 48 

Inspection, Addition and sub- 
traction of fractions by 2 45 

Instructional questions 5 125 

Interest 2 78 

" Annual 2 87 

" Compound 2 88 

" Exact 2 86 

" formulas 2 78 

" in history increased by 

public libraries 6 36 

" laws of Canada 2 94 

" " " United States. ... 2 95 

" Short methods in 2 92 

Interjection not a part of speech 4 88 

The 4 88 

Interjections, Division of, into 

classes 4 89 

" generally echo 

the sense 4 88 

Intermediate arithmetic 1 4 

Interrelations of subjects of 

study 6 64 

Interrogative adjectivepronouns 4 15 

" adverbs 4 76 



Sec. Page. 

Intransitive verbs. Active 4 35 

Invention by Fulton 7 21 

Inverting the divisor 2 54 

Irregular verbs 4 32 

" " Drill with 4 41 

" " Remarks on 4 31 

J. Sec. Page. 

Journal, Library- 6 37 

Iv. Sec. Page. 

Klemm, Dr C 48 

Know subject. Teacher must 6 10 

Knowledge of subjunctive mode 4 48 
" " words. Nature of 

our 3 63 

L,. ^'<v. Page. 

Labor, Division of, in teaching. . 6 62 

Laboratory method. The 6 34 

Language, Chinese 7 3 

" Definition of 3 1 

" lesson, Everj^ lessoti a 1 71 

" lessons 3 5 

" of number. Impor- 
tance of 1 41 

Later fraction work 1 53 

" lessons in map-sketching 5 KX) 

Latest textbooks. The 3 5 

Latin prefixes 4 26 

Law of sequence. General 3 .53 

Leap years 2 113 

"Learn to do by doing" 7 40 

Learning history, how it is usu- 
ally done 6 n 

" rules and definitions.. 1 62 

" words. Method of 3 W 

Least common multiple by divi- 
sion 2 44 

Least common multiple bj- fac- 
toring 2 42 

Least mental resistance 3 .55 

Lecture method. Remarks on the 6 40 

The 6 38 

Legislature of Massachui5etts .. . 7 16 

Leibnitz 1 44 

Lesson, A model 5 119 

" in German school, A 

specimen 6 ■ 48 

" " orthography. Gen- 
eral treatment of . . 7 67 

Lessons in abbreviations 7 83 

" Preparation of 6 17 

" Preparation of, from 

textbooks 6 20 

" Summary of 5 121 

" with halves and thirds. . 1 51 

Letters, Form and matter of 7 98 



INDEX. 



Sec. 
Letters, Names of, and how to 

write 7 

Lever of Archimedes 5 

Liable to be mispronounced, 

Words 7 

Liberal sciences. The 5 

Libraries increase interest in 

historical study 6 

" Library Journal " 6 

Life, Educational value of out- 
door 5 

" the earth as abode of 5 

Limit, The word 3 

Linear units 5 

List of prepositions 4 

" " words 7 

Living, Complete 5 

Location on a plan 5 

Locomotive, The first 5 

Long columns, Addition of 2 

" division, French method of 2 
Lower school grades, Natural 

science in 5 

Lucrative sciences, The 5 

M. Sfc: 

Macaulay 1 

Making and recording observa- 
tions 5 

Manner of educational progress 3 

Man's place in science 5 

Map in recitation 5 

" of bicycle trip 5 

" reading 5 

" sketching 5 

" " Later lessons in 5 
Map-drawing, Intermediate 

view of 5 

Mapping and analysis. Selections 

for 3 

" sentences 3 

Maps, Government survey 5 

" Stencil 5 

" The making of •') 

" Wall 5 

Mariner's compass, The 5 

Mark of exclamation 3 

Marks, Diacritical 7 

Massachusetts, Legislature of .. . 7 

Matter and method in geography 5 
Matters connected with the 

study of the noun 3 

Maxim of Comenius 5 

Meaning, Adverbs classified with 

respect to 4 

" of correlation 6 

" " etymology 3 



4 
23 

84 
15 

36 
37 

54 
35 

38 
71 
82 
82 
16 

20 
1 
4 

60 
15 

Page. 

18 

81 
6 

38 
118 



36 
24 

107 

101 
05 

117 
75 
16 
56 
16 

108 



Meaning of noun 

" " relation 

" "Shall" and "Will " 

" " suffixes 

" " terms 

" " the term syntax 

Means and extremes among 

words 

Measurement, Angular 

Measures and their applications 
Measuring and constructing an- 
gles 

Mementoes, Relics and 

Memorizing rules, principles, etc. 

Mensuration 

" Formulas in 

Mental demand for course and 
consequence of action 
" demand for time of ac- 
tion 

" discipline and utility 

" resistance. Least 

Mercator's projection 

Meter 

Method, Biographical 

" Catechetical 

" Comparative 

" Cooperative 

" Eclectic 

" Grube 

" Improvement of 

" Laboratory 

" Lecture 

" Memoriter 

" necessary in stud\' and 

teaching 

" of analysis, Remarks on 
" " interest. The seven- 
ty-day 

" " learning words 

" " securing ends of spec- 
imen lesson 

" " Socrates, The 

" " treating etymology 

and syntax 

" " work compared to 

amount of 

" Seminary 

" Sight or " Flash " 

" Topical 

Methodology 

Methods, Description of 

" Explanation of 

" in orthography 

" Many, in history 

" Need for exact and 

iiniform 

" Observations upon 



Sec. 


Pag 


3 


70 


4 


1 


4 


67 


7 


87 


3 


37 


3 


10 


4 


•23 


5 


73 


5 


68 



76 

no 

110 



6 


42 


7 


61 


3 


56 


5 


77 


2 


116 


6 


41 


6 


27 


C 


.52 


6 


.55 


i; 


.57 


1 


7 


3 


.50 


6 


34 


6 


38 


6 


29 


6 


14 


3 


35 


y 


s:b 


3 


04 


6 


40 


r> 


128 



1 


70 


6 


.56 


7 


72 


6 


31 


6 


26 


6 


26 


7 


74 


7 


82 


6 


27 


7 


18 


6 


59 



INDEX. 



SfC. Pii.iTi'. 



Methods of interest by aliquot 

parts 

" " percentage 

" " procedure 

" " teaching evolution.. 

" " " h i s t o r y , 

Other. . . . 
" Remarks on lecture . . . 

'^' Success of, determined 

by use 

" Summary of 

Metric System 

" " Abbreviations in 

Mill, John Stuart 

" " " Political econ- 
omy of 

Miscellaneous collections of 

specimens 

" operations and 

suggestions 

Mispronounced, Words liable to 

be 

Misuse of certain prepositions.. . 

Mixed abbreviations 

" numbers. Multiplying 

Modal adverbs 

Mode, Definition of subjunctive 
" Examples of subjtinctive 

" Imperative 

" Infinitive 

" Necessary knowledge of 

subjunctive 

" Potential 

" Subjunctive 

Model lesson, A 

Modeling materials 

Models of analysis 

Modes, Functions of the 

" Indicative 

" of verbs 

" " " Remarks on 

Modification, General 

" in grammar 

" of words 

Modified, Neuter verbs cannot 

be 

Modifiers 

" The noun w^ith 

" Modify," The word 

Monitor and Merrimac 

Much used. Any method monot- 
onous if 

Multiplication, Drills for 

" of denom in a te 

numbers 

" Proofs of 

". Short methods in 
" Unwritten 



•z 


8:i 


2 


ri 


5 


69 


3 


98 


G 


55 





38 


r 


29 


6 


60 


2 


115 


2 


ro 


■5 


21 



30 

84 
48 
34 
49 

47 
49 
46 
51 

48 
44 
46 
119 
106 
29 
45 
44 
43 
43 
39 
37 
20 

74 

;k 

71 
37 



Sec. Page. 
^Multiplication, Unwritten, by 

two figures 2 8 

'• without partial 

products 2 9 

Multiplier of special form 2 8 

" slightly greater than 

10, 100, etc 2 12 

Multiplying by aliquot parts 2 13 

Museum, The National 5 63 

My thologj', Scandinavian 6 50 

X. Sec. Page 
Nature of our knowledge of 

words 3 63 

Need for care in the use of rela- 
tives 3 44 

" " mark of exclamation. 

Slight 3 16 

Neuter and active. Verbs that 

are 4 75 

" verbs 4 38 

" " cannot be modi- 
fied ■. ... 4 74 

Newlv coined verbs are regu- 
lar." 4 33 

Notation and numeration 1 38 

Arabic 1 38 

" Common method of 1 42 

" Decimal base of 1 44 

" Roman 1 46 

" Scientific method of... 1 42 
" Two methods of teach- 
ing 1 42 

Noun, Definitions of 3 70 

" Meaning of 3 70 

" Other matters connected 

with the study of the. . . 3 72 

Table of 4 1 

The 3 70 

" with inodifiers, The 3 71 

Nouns, Abstract 3 76 

" Cases of 3 81 

" Classes of 3 74 

" Collective 3 76 

'• Gender of 3 78 

" Inflection of 3 76 

" Number of 3 78 

" Person of 3 7'7 

" Sin' generis 3 75 

" Verbal 3 76 

Number of cases 4 2 

" " nouns 3 78 

Numbers, Divisibility of 2 33 

" Perception of 1 38 

" Properties of 2 33 

Numeral adjectives 4 14 

Numerals, Cardinal 4 15 

Ordinal 4 15 



XX 



INDEX. 



O. Sec. Pafre. 
Objection to specialization in 

training 6 63 

Objectionable words, Getting 

rid of 3 65 

Objections to correlative work. . 7 99 

" " decimal base 1 45 

Objective, Adverbial 4 78 

Objects, Experiment with 1 14 

" How to use 1 2 

Observation, Orderly 5 50 

Observations, Making and re- 
cording 5 81 

" on sun's apparent 

motion 5 93 

" upon methods. .. . 6 59 

Obstacles to a perfect alphabet 7 11 
Obtaining words for spelling 

work, Means of 7 62 

Office and denotation of the ad- 
jective 4 10 

" of the adverb 4 73 

Omissions from textbooks 3 8 

Omitted elements 4 36 

One, The number 1 72 

Operations and suggestions. Mis- 
cellaneous 2 30 

" The formulating of. . 2 32 
Opinions, Diverse, concerning 

value 5 6 

Opposites, Defining by 7 74 

Oral and written spelling 7 45 

Order of sentential elements ... . 3 51 
" " subjects in denominate 

numbers 2 59 

" " topics in fractions 1 54 

Orders, Teaching of 1 43 

Ordinal numerals 4 15 

Original examples by pupils .... 1 61 

Orthography, Definition of 7 1 

" General treat- 

ment of lesson 

in 7 67 

" learned from 

reading 7 59 

" Methods in 7 82 

Other expressions of comparison 4 22 

" forms of pleonasm 3 59 

" methods of teaching his- 
tory 6 55 

" transitive forms 4 37 

Our knowledge of words. Nature 

of 3 03 

" needs with reference to 

words 7 43 

Outdoor life, Educational value 

of 5 .54 

Outline of geography. Funda- 
mental 5 36 



P. Sec. 

Paragraph spelling 7 

Parent is the child's first teacher 5 

Parsing, Etymological 3 

Part of speech. Interjection not a 4 
" " the infinitive. Sign "to" 

as 4 

Partial payments 2 

" " Rules of, com- 
pared 2 

Participial adjective 4 

Participle and infinitive. Simi- 
larity of the 4 

" The future 4 

Participles, Classification of 4 

" Degrees of predica- 
tion by 4 

" Remarks on table of 4 

Table of 4 

The... 4 

Passages, Writing beautiful or 

striking 7 

Passive progressive tense forms 4 

Past emphatic tense forms 4 

Pedagogics defined 1 

" of arithmetic 1 

" number percep- 
tion 1 

" The word 1 

Pedagogue, A Greek 5 

" Greek 1 

Percentage 2 

" Applications of 2 

" Decimal method of 2 

" Formula method of 2 

" Fraction method of 2 

" Importance of 2 

Percentage, Three methods of.. 2 

Perception 5 

" of number 1 

" Use of 5 

Perceptions, The earliest sense.. 5 

Perfect alphabet, A 7 

" " Obstacles to.. 7 

Period with abbreviations. The 7 
Person mentioned, " Shall " and 

"Will" denoting will of 4 

" of nouns 3 

Personality of teacher an ele- 
ment of success 7 

Pestalozzi 1 

Philological Association, Amer- 
ican 7 

Phonies, The study of 7 

Phrases 4 

PliN-sical science the essence of 

geography 5 

Pictured comparisons 5 

Pictures, Concepts from 5 



Page. 
46 
52 
80 

88 

54 



73 

71 
71 
44 
38 
46 
49 
6 
11 
35 



50 
5 

10 
85 
80 

37 
102 
57 



INDEX. 



Sec. Page. 

Pictures, Geography in 5 55 

" Preparation of 5 58 

" Spelling from 7 915 

" Value of, in acquiring 

a vocabulary 5 59 

Place, The element of, in geog- 
raphy 5 78 

Plan of classroom 5 79 

" *" paper 1 6 

" " primary work 1 71 

" " teaching fractions 1 -19 

" " treating the verb 4 29 

Plane, Location on 5 77 

Pleasure and pain. Theory of ... . (J 5 

Pleonas:n 3 58 

Other forms of 3 59 

Pliny's Geography 5 3{i 

Pluralizing abbreviations 7 3G 

Plurals of symbols 7 G 

Plutarch, Parallels of 53 

Poe, Edgar A., Praise words of . . 6 2 
Poems and ballads. Historical 

use of (5 23 

Points in teaching geography .. . 5 113 

Position of the adverb 4 78 

Positive degree of adjectives. .. . 4 19 

Possessive adjective pronouns.. 4 15 

" pronouns. Absolute. . 6 G 

Potential mode. The 4 40 

Power of inference. Test of G 44 

Precedence of signs 2 29 

Predicate complement 3 33 

" compound 3 23 

" Subject and 3 26 

The 3 32 

Predicating and assuming action 4 43 
Predication by participles. De- 
grees of 4 57 

Prediction, " Shall " and " Will " 

denoting a 4 71 

Prefi.ses, Anglo-Saxon 4 25 

" by antonyms 4 19 

Greek 4 27 

Latin 4 2G 

Preliminar J- questions 5 124 

" remarks on the verb 4 29 

Preparation for teaching history G 14 

" of lessons G 20 

Preposition, Definition of the 4 79 

" Sign "to" regarded 

as a 4 53 

Table of the 4 83 

Prepositions, Exercises with. .. . 7 97 

" Government by. . . 4 81 

" List of 4 83 

" Misuse of 4 84 

" Use of, with cer- 
tain words 4 83 



Sec. 

Prepositions, used adverbially.. 4 

Present emphatic tense forms. . . 4 

" tenses, The 4 

Primary and secondary accents 7 
" and secondary educa- 
tion one scheme 5 

" arithmetic 1 

" teaching 1 

" work in detail 1 

Prime numbers. Table of 2 

Test for 2 

Principle in teaching, A general G 
Principles and materials in spell- 
ing, 7 

" concerning signs 2 

" of the lesson. Underly- 
ing G 

" . of Roman notation 1 

Procedure, Method of 5 

Processes in denominate num- 
bers 2 

Progress, Manner of educational 3 

Progressive passive. Forms of.'. . 4 

Projection, Mercator's 5 

Promise, "Shall" and "Will" 

denoting a 4 

Pronominal adjectives 4 

Pronoun, Classes of 4 

" Definition of 4 

" Demonstrative 4 

Indefinite 4 

" Interrogative 4 

Personal 4 

" Relative 4 

Table of the 4 

The 4 

Pronouns, Absolute Possessive.. 4 

" Adjective 4 

" Ambiguity from useof 4 

" Compound 4 

Pronunciation, Variant 7 

Proofs of addition 2 

" " division 2 

" "multiplication 2 

" "subtraction 2 

Proper adjective 4 

" use of short methods 2 

Properties of numbers 2 

Proportion 2 

" Transformations of.. 2 

Prose and poetry quotations 6 

Prosody S 

Protractor, The 5 

Public libraries increase interest 

in history 6 

Punctuation and capitals 3 

" in classification of 

sentences 3 



Page. 
81 
63 
59 



26 
28 
26 
26 
13 
6 

a3 

96 
96 
12 
13 
74 

36 
14 



XXll 



INDEX. 



St'c. Page. 

Punctuation, Wilson's 7 ~G 

Pupil's vocabularies, Enlarging 3 00 

Pure n u ui ber, The 1 'i% 

Purpose of addition drill 1 28 

" drills 1 28 

" " history study G 9 

" "specimen lesson, 
Method of secur- 
ing 49 

" " subtraction drill 1 30 

Psychological use of rules 7 89 

" value of geogra- 
phy 5 22 

Q. Sec. Page. 

"Qualify," The word 3 38 

Qualitative adjectives 4 14 

Question and answer recitation. 

The 6 19 

Questioning, The art of 5 123 

Questions, Classification of 5 124 

" Didactic or instruc- 
tional 5 125 

" Preliminary or ex- 
perimental 5 124 

" Testing or examina- 
tion 5 125 

Quotation from Brown's gram- 
mar 4 31 

" " Cobbett's gram- 
mar 4 31 

Quotations, Prose and poetry 12 

R. Sec. Page. 

Rates in interest. Changing 2 85 

Ratio of oral to written work ... 1 CH 
Reading, Historical and bio- 
graphical 6 14 

" Map 5 115 

" Orthography learned 

from 7 59 

" Teacher should regu- 
late 6 11 

Reasons why history should be- 
gin early 51 

Recitation, Map 5 118 

" of history. The usual 18 
" The question and an- 
swer 6 19 

" The verbatim C 18 

Recreations, Historical 6 25 

Reduction ascending 2 63 

" descending 2 61 

" of radicals 2 102 

Redundant verbs 4 35 

Reference books in country dis- 
tricts 6 10 

" Books of 5 132 



Sec. Page. 
Reference to time by subjunc- 
tive mode 4 50 

Reform, Spelling 7 9 

Regular, Newly coined verbs are 

always 4 33 

" verbs 4 32 

Relation of adverbs and adjec- 
tives to verbs 4 73 

" " history to other sub- 
jects 6 61 

" " scisnce to human 

needs 5 30 

" What is meant by 4 1 

Relative, The, " what " 4 8 

Relatives, Need for care in use of 3 44 

Relics and mementoes 6 22 

Remarks on classes of questions 5 125 
" " classification of sen- 
tences 3 56 

" " enlargement of vo- 
cabulary 3 66 

" " illustrative lesson .. 6 49 

" " method of analysis 3 35 

" " modes 4 43 

" " objections to correl- 
ative work 7 99 

" " report of "Commit- 
tee of Fifteen" ... 6 07 
" " table of adjectives. . 4 17 
" " the irregular verb. . 4 34 
" " " lecture method 6 40 
" " verb. Prelimi- 
nary 4 29 

" "Topical" 33 

Reminiscence, A 5 126 

Repetition, Necessity for drill 

and 7 05 

Report of "Committee of Fif- 
teen" 5 24 

Requirement, An early 5 68 

Resistance, Least mental 3 55 

Resolutions of Geographical 

Congress 5 96 

Responsives 4 77 

Restrictive clauses, -'\mbiguity 

from 3 41 

Review of details in analysis .:. . 3 32 

Reviews 6 24 

" should be frequent 1 37 

Rhetoric 3 12 

Right-angled triangles 2 114 

Robinson Crusoe 6 44 

Roman notation 1 46 

" " Inferiority of .. . 1 46 

" " Principles of ... . 1 47 

Root, Cube 2 100 

Fourth 2 101 

- " Square 2 100 



INDEX. 



Si'c. Pifg'c. 

Roots of fractions 3 101 

Rousseau, Quotation from 5 O'J 

Rule, Euclid's x! 114 

" Merchant's i SO 

" Plato's -i 111 

" Pythagoras' ~ 111 

" United States i 89 

Rules and definitions, Learning- 

- of 1 62 

" for compounding words. . . 7 'Hi 

'• " spelling (■ 04 

" " syllabication 7 15 

" formulated T 25 

" Grammatical ~ 23 

" of spelling 7 77 

" " " Exercises with 7 90 
" principles, etc., Memoriz- 
ing 7 76 

" Psychological use of 7 89 

S. Sec. Page. 

Sailor geography 5 109 

Salamis, Battle of C 47 

Sand modeling 5 106 

Saxon words 3 17 

Scale, Plan of classroom drawn 

to 5 79 

Scandinavian mythology 50 

Scheme of division drill. General 1 35 
" " " " in detail 1 35 
" fraction work. Re- 
marks on 1 00 

.Schemes of drill for blackboard 1 28 

Science, Abbreviations used in. . 7 30 

" Collections in natural . . 5 00 

" distinguished from art 1 2 

" Plan's place in 5 38 

" Natural, in lower school 

grades 5 00 

" Relation of, to human 

needs 5 30 

Sciences, The " Bread-and-But- 

ter " 5 15 

" The liberal and the lu- 
crative 5 15 

•Scientific facts must be discrim- 
inated 5 111 

Selecting books for spelling 7 49 

Selection of words, Sources of.. 7 42 
" " " Two objects 

determine 7 42 
•Selections for mapping and anal- 
ysis 3 30 

Semiuaria 6 40 

Seminary method. The .50 

Sensation 5 42 

" and perception 5 40 

Sensations classified 5 43 



Sec. Page. 

Sensations, The earliest 5 48 

Sense, Development of hislt)ric.. 6 45 
" perceptions. The earliest 5 48 

■' training, Need for 5 41 

Sentence, Analysis of 3 36 

building 3 48 

" Complex 3 24 

"" Compound 3 23 

" Simple 3 21 

" Simple, with com- 
pound predicate 3 23 

" Simple, with com- 
pound subject 3 22 

" Simple, with com- 

pound subject and 

predicate 3 23 

" spelling 7 40 

The 3 17 

Sentences classified with respect 

to form 3 20 

" classified with respect 

to use 3 18 

" Connectives in classi- 
fication of 3 57 

" Exclamatory 3 19 

" in composition 3 12 

" Punctuation in classi- 
fication of 3 57 

" Summary of classes 

of 3 .56 

Sentential elements. Compara- 
tive importance of 3 09 
" elements. Order of . . 3 51 

.Sequence, General law of 3 53 

Serial adjectives 4 24 

" discoiints 2 70 

Sex and gender 3 81 

.Shakespeare 7 5 

"Shair'and "Will" 4 67 

" " " Collection of 

examples 

with 4 72 

" " " denoting a 

prediction 4 71 
" " " denoting a 

promise or 

threat 4 71 

" " " denoting de- 

ter m ina- 

tion 4 08 

" " " denoting fu- 
turity 4 70 

" " " denoting 
person 
mentioned 4 09 
" " " denoting 
will of 
hearer 4 69 



XXIV 



INDEX. 



SfC. PdJl'C. 



Sec. 



"Shall" and "Will" d e n o t i n g 
will of 
higher 

power 4 

" " " denoting 
will of 
speaker ... 4 
" " " Fundamen- 
tal mean- 
ing of 4 

Short methods in division 2 

" " " interest 2 

" " " multiplication 2 

" " Proper use of 2 

" words that are often mis- 
spelled 7 

Sight or "Flash" method in 

spelling 7 

Sign of the infinitive 4 

" "to" as part of the infinitive 4 

" " regardedaspreposition 4 

Signs, Precedence of 2 

Principles concerning 2 

" Use of 1 

" used in fundamental rules 2 
Similarity of terms of the indica- 
tive mode 4 

" " the participle and 

infinitive 4 

Simple adverbs 4 

Simultaneous addition and sub- 
traction 2 

Singsong, How to avoid 1 

Six-per-cent. method 2 

" Six," The number 1 

Sixty-day method of interest ... 2 

Sketching map 5 

Slight need for marks of ex- 
clamation 3 

Societies, titles. Names of, abbre- 
viated 7 

Socrates as a teacher 5 

" The method of 5 

Socratic dialogue, Another speci- 
men of 5 

Sounds, Coalescence of 7 

Speaker, "Shall" and "Will" 

denoting will of the 4 

Special cases in addition and sub- 
traction of fractions ... 2 

" constructions 3 

" multipliers 2 

Specialization in education 5 

" " training, O b- 

jections to. . . 6 
Specimen lesson in German 

school 6 

Specimens, Serial 5 



60 



3(i 

127 
128 



Speech, Interjection not a part of 

Speller's instinct. The 

Spelling, Article in " Forum " on 

" as taught years ago. .. . 

" Column 

" Concerning rules for . . 

" Correlation of, with 
general information 

" Correlations of 

" Exercises with rules of 

" from pictures 

" General considerations 



" Heredity in 

" Oral and written 

" Paragraph 

" Principles and mate- 
rials in 

" reform. 

" Use of a textbook in 
teaching 

" work. Means of obtain- 

mg words for 

Spencer, Mr. Herbert 



Sphere 

Square root 

Squares 

Stage, A critical 

Standard dictionary. 

State and action 

Stencil maps 



Stories, Arithmetical. 



Studies, General classification of 
Study and teaching, Method 

necessary in 

" of composite numbers. . . 
" " history. Children dis- 
like 

" " " Purpose of. . . 

" " phonics. The 

" " the noun. Matters con- 
nected with the 

" Value of grammatical 

Subdivided unit, The 

Subject and predicate 

" of the infinitive 

" Teachers must know. . . 

The 

Subjects of study. Interrelations 

of 

Subjunctive mode, Definition of 

" " Examples of 

" " has slight 

refer en ce 

to time 



Pasre. 
88 
38 
51 
37 



100 
80 
90 
96 

37 
40 
45 
46 



62 

16 

. 70 

112 

100 

12 

51 

10 

38 

101 

102 

22 

53 

10 

14 

85 

6 
9 

85 

72 

4 

74 

26 
51 
10 
32 

64 
47 
50 



INDEX. 



Sec. Pajfi'. 
Subjunctive mode, Knowledge 

teachers should have of 4 48 

Subjunctive mode, The 4 46 

Subordinatmg conjunctions 4 87 

Subtracting, Two methods of... 2 2 
Subtraction drill, General scheme 

of 1 31 

" " Purpose of 1 30 

Drills for 1 30 

" of denominate 

numbers 2 04 

" Proofs of 2 20 

Success, Conditions of, in teach- 
ing history 58 

'■ depends on use 7 19 

" Teacher's personality 

an element of 7 50 

Suffixes, Alphabetical arrange- 
ment of 7 87 

"■ Exercises with 7 88 

" in teaching, The use of 7 86 

" Meaning of 7 87 

Sui generis nouns 3 75 

Summary of lessons 5 121 

" on methods 60 

Sun's apparent motion. Obser- 
vations on 5 93 

Superlative and comparative. 

Forms of the 4 28 

" degree of adjec- 
tives 4 21 

Surface units 5 71 

Survey maps. Government 5 107 

Surveying with bicycle and cy- 
clometer 5 83 

Syllabication 7 12 

" Degrees of diffi- 
culty in 7 13 

" Exercises in 7 14 

" in spelling 7 16 

" Rules for 7 15 

Symbol of operation in multipli- 
cation 2 11 

Symbols and their plurals 7 6 

" Conditionsexpressedby 1 21 

Synonjnns, Defining by 7 74 

" Works on 7 74 

Synopsis of all tenses 4 63 

Syntax and etymology. Method 

of treating 3 68 

" and etymology should 

be treated together.. 3 69 
" Collections of, for cor- 
rection 3 62 

" Etymology and 3 67 

" Examples of false 3 61 

" Meaning of term 3 10 

Synthesis 3 46 



Sec. Page. 

Synthesis, Exercise in 3 49 

" Exeicise in, for m- 
creasing vocabu- 
lary 3 47 

" of complex sentences 3 54 
" "sentential ele- 
ments 3 46 

System, The metric 2 115 

T. Sec. Page. 

Table of the adjective 4 10 

" " " " Remarks 

on 4 17 

'• " " adverb 4 79 

" " " conjunction 4 88 

" " " noun 4 4 

" " " participle 4 57 

" " " preposition 4 85 

" " " pronoun 4 10 

" " " verb , 4 72 

Tables of prime numbers 2 30 

Tabular classification of sen- 
tences 3 56 
" " Remarks 

on 3 .56 

"Tale of Two Cities" 6 15 

Taste for historical and bio- 
graphical reading (i 14 

Teacher, Illicit assistance by the 7 18 

" miist know his subject 6 10 
" should have knowledge 

of subjunctive mode 4 4S 
" should regulate his 

reading. How 6 11 

" Socrates as a 5 127 

The child's first 5 52 

" " wheelman as a 5 82 

Teaching geography, Cause and 

effect in 5 122 

" geography, Some 

points in 5 113 

" history. Difficulty in. . . 6 8 

" " Preparation for 11 

" effractions 1 48 

" " " Conditionsof 

success in 1 49 
" orthography, The col- 
lecting of devices for 7 63 
Teachers at Vienna, Views of... 5 97 

Tense, Definition of 4 58 

" forms. The passive pro- 
gressive 4 02 

" of all modes, Summary of 4 03 

The future 4 01 

" past 4 01 

Tenses, The present 4 59 

Term "active" as used in gram- 
mar 4 40 



XXVI 



INDEX. 



Sec. Page. 
Term "correlation," Meaning of 

the 65 

" denoted by the infinitive. . 4 55 

Terms, Meaning of 3 37 

used by writers on gram- 
mar 3 70 

Test for prime numbers 2 35 

" of geographical value 5 31 

" " power of inference 6 44 

" words in spelling 7 102 

Testing questions 5 125 

Textbook, Geography without a 5 08 

Textbooks 3 5 

" and methods, Value of 3 7 

" Evolution of 5 112 

" for spelling. Selection 

of 7 49 

" in teaching spelling, 

Use of 7 47 

" Omissions from 3 8 

" on history 6 

" Preparing lessons 

from 6 20 

The latest 3 5 

" What, should contain 3 9 

That, who, and which 3 42 

The number "one" 1 72 

Theory modified by fact 5 IG 

" of pleasure and pain 6 5 

Things distinguished by differ- 
ences 5 40 

Thought, Forms of written 1 

"Three," The n\imber 1 75 

Thurot, Quotation from 7 69 

Time given to history 6 13 

" or action. Demand for 6 42 

" Subjunctive mode has 

slight reference to 4 50 

To multiply bya number slightly 

greater than 10, 100, etc 2 12 

" subtract by adding 2 3 

Topical, Extension of meaning of 6 32 

" method 6 31 

" Remarks on 6 33 

Topics, Order of, in fractions. ... 1 54 
Topographical map, Description 

of 5 107 

Training, Objections to special- 
ization in 6 63 

Transformations in proportion.. 2 96 

Transitive forms, Other 4 37 

" When a verb is 4 .37 

Travel and adventure. Books of 5 1-33 

" " geography, Books of 5 134 
Treatment of etymology and sj-n- 

tax. Method of.... 3 C7 
" " lessons in orthog- 
raphy, General.. . 7 67 



Treatment of thenoun, Gradation 

of 3 

" " ' verb. Plan of.. . 4 

Triangles, Right-angled 2 

True discount 2 

Truth, Demand for, m narrative 6 

"Two," The number i 

Tyndall, John 5 

" 6 

Type formulas 1 

Types of examples 1 

U. Sec. 

Ultimate basis of science 5 

Ul y sses 5 

Underlying principles of the les- 
son 6 

Unilineal writing 6 

Unit, Fractional 1 

" of thought. The 3 

The subdivided 1 

United States, Rule of partial 

payments in. . 2 
" " topographical 

maps 5 

Units, Linear 5 

" Surface 5 

Unity of primary and secondary 

education 5 

University, Harvard 7 

Unnecessary compounds. Avoid 7 

Unwritten multiplication 2 

" " by two 

figures 2 

Usage, Common 3 

" Established 7 

Use, Adverbs classified with re- 
spect to 4 

" and abuse of abbrevia- 
tions 7 

" determines success.. 7 

" of apparatus 1 

" " a textbook in spelling 7 

" " formulas in interest 2 

" " hyphen 7 

" "perceptions 5 

" " pictures in teaching 5 

" " poems and ballads. His- 
torical 6 

" " prepositions with certain 

words 4 

" "'pronouns. Ambiguity 

from 4 

" " relatives, Care in the 3 

" "rules. Psychological 7 

',' " signs 1 

" " " in fundamental 

operations 2 



Sec. Page. 



70 
29 
114 
93 
41 
73 
37 
56 
25 
23 

Page. 
36 
22 

48 

6 

8 
17 
74 

89 



XXVll 



Sec. Pag-c. 

Use of suffixes in teaching 7 8(i 

" " type formulas 1 25 

" Sentences classified with 

respect to 3 18 

Usefttl drill in fractions 1 (>•"> 

Utilitarianism, Abuse of 7 41 

Utility and mental discipline 7 01 

X. Sec. Page. 

Value, Educational 5 1 

" " affected by 

existing 

conditions 5 8 
" " Diversity of 
opinion 

concerning 5 G 

" in general 5 1 

" is relative 5 2 

Value of exactness and thor- 
oughness 3 40 

" " geography, Dr. Har- 
ris's estimate of 5 21 

" " geography, Psycho- 
logical 5 22 

" " grammatical study... 3 4 
'■ " textbooks and meth- 
ods 3 7 

" Test of, in geography 5 31 

Vastness of history til 

Verb, Definition of the 4 30 

" Plan of treatment of the 4 29 
" Preliminary remarks on 

the 4 20 

Table of the 4 72 

The 4 20 

" when transitive 4 37 

Verbal nouns 3 70 

Verbs, Active and intransitive. . 4 3r) 

" " transitive 4 3.5 

" as related to adjectives 

and adverbs 4 73 

" Auxiliary 4 GO 

" Classification of 4 32 

" Defective 4 35 

" Drill with irregular 4 41 

" Modes of 4 43 

" " " Preliminary re- 
marks on 4 43 

Neuter 4 38 

" " cannot be modi- 
fied 4 74 

" Newly coined, are alwaj'S 

regular 4 33 

" Redundant 4 35 

" Regular and irregular. . . 4 32 
" Remarks on classification 

of 4 40 

" " " irregular 4 34 



Sec. Page. 

Verbs, Tenses of 4 58 

" that are both active and 

neuter 4 75 

Vienna, Views of teachers at. .. . 5 07 
Vocabularies, Enlarging pupils' 3 GO 
" Remarks on en- 
larging 3 CO 

Vocabulary, Acquiring a 3 03 

" Synthetic exercise 

for increasing. . . 3 47 
V^ocabulary, Use of pictures in 

acquiring 5 .59 

Voluntary attention 1 4 

Von Humboldt 5 32 

Von Ranke, Leopold G .55 

"NV. .Sec. Page. 

Wall maps 5 117 

What are abbreviations ? 7 33 

" is meant by relation 4 1 

" textbooks on grammar 

should contain 3 9 

" The relative ' 4 8 

" to omit from textbc^oks on 

grammar 3 8 

"What words say " 7 70 

Wheelman as a teacher, The 5 82 

When a verb is transitive 4 37 

White, Richard Grant 7 8 

Whitney, William D 7 10 

Who, which, and that 3 42 

Whole, The earth as a 5 34 

"Will "and "Shall" 4 07 

" Will " and " Shall " denoting 

determination 4 OS 

"Will" and "Shall," Funda- 
mental meaning of 4 07 

Will of the hearer, " Shall " and 

"Will" denoting 4 00 

" of the person mentioned, 
"Shall" and "Will" de- 
noting 4 00 

" of the speaker, "Shall" and 

" Will " denoting 4 08 

Wilson, "Punctuation" by 7 20 

Word "limit," The 3 38 

" lists, Devices and 7 82 

" "modify," The 3 37 

" "qualify," The 3 38 

Words belonging to a given en- 
vironment 7 95 

" Compounding of 7 20 

" Defining, in connection 

with spelling 7 73 

" denoting collections 7 03 

" " different as- 

pects of the 

same idea ... 7 04 



XXVlll 



INDEX. 



Sec. Page 
Words, Extremes and means 

among 4 23 

" for spelling. Select ion 

of r 42 

" " " Sources of 

selection 

of r 42 

" " " work, Means 
of obtain- 
ing 7 02 

" Getting rid of objection- 
able 3 05 

" in common use 7' 58 

" spelling, Test of 7 102 

" liable to be mispro- 
nounced 7 84 

" Method of learning 3 04 

" Modification of 7 20 

" Nature of our knowledge 

of 3 03 

" Pupils should copy 7 08 

" " " pronounce 7 07 

" " write,from 

dictation 7 OS 



Sec. Page. 

Words, Saxon 3 17 

Work, A daily 4 42 

Works on English synonyms. ... 7 74 
Writers on grammar. Terms 

used by 3 70 

Writing beautiful or striking 

passages 7 71 

Bilineal 4 

" Multilineal 4 _ 

" same word often, Effect 

of 7 09 

" Unilineal 4 

Written forms in fractions 2 40 

" spelling 7 45 

" thought. Forms of 1 

X. Sec. Page. 

Xerxes' invasion of (Ireece 47 

Y . Sec. Page, 

Years, Leap 2 113 

" work 1 09 

Z. Sec. Page. 

Ziller 50 



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